I don’t think there is a difference in the actual moment of compassion, it’s just compassion. It’s the same no matter what your religion, or none. There are differences in how you conceptualize it afterwards perhaps. A Buddhist might see it as a brief moment of non confusion and of connection with what is true, grounding and wholesome. Or might say it is a moment when you were inspired and blessed by the compassionate nature of Buddhas, and connected to the Buddha nature in all of us. Might conceptualize it in many ways.

With Buddhists as for Christians it is not something you do out of a motivation to help yourself. If you do it like that, it’s not true compassion.

All the main branches of Buddhism are like this. It’s not just the “Mahayana” schools, they teach more this way, but a “Mahayana practitioner” can easily end up practicing compassion to help themselves, which is not really true compassion. And a Therevadan practitioner likewise, just through connecting to the truth and authenticity of their situation might well be opening to compassion and loving kindness in a simpler and more direct way.

The path of Therevada of connecting to truth is a path of opening out to others and of compassion too. All the quotes here are from Walpola Rahula’s “What the Buddha Taught” which describes the central teachings of Therevadan Buddhism, and talking about the Noble Eightfold Path which is central to Therevadan Buddhism:

“Ethical Conduct (Si/a) is built on the vast conception of universal love and compassion for all living beings, on which the Buddha's teaching is based. It is regrettable that many scholars forget this great ideal of the Buddha's teaching, and indulge in only dry philosophical and metaphysical divagations when they talk and write about Buddhism. The Buddha gave his teaching 'for the good of the many, for the happiness of the many, out of compassion for the world' “

“According to Buddhism for a man to be perfect there are two qualities that he should develop equally: compassion {karuna) on one side, and wisdom (panna) on the other. Here compassion represents love, charity, kindness, tolerance and such noble qualities on the emotional side, or qualities of the heart, while wisdom would stand for the intellectual side or the qualities of the mind. If one develops only the emotional neglecting the intellectual, one may become a good-hearted fool; while to develop only the intellectual side neglecting the emotional may turn one into a hardhearted intellect without feeling for others. Therefore, to be perfect one has to develop both equally. That is the aim of the Buddhist way of life: in it wisdom and compassion are inseparably linked together, as we shall see later. “

All the main schools of Buddhism - the ones that treat the ancient Buddhist sutras as the authentic teachings of the Buddha - have their own versions of most of the early teachings. These are almost identical with only minor changes, so these schools have large numbers of sutras in common. What he says in the quotes here are accepted by all the main schools of Buddhism.

Buddhism isn’t really about trying to get a good life through karmic cause and effect. Well it is up to a point. Buddha encouraged us to be kind to ourselves :). If we can find a way to be happy in this world for a while, there’s nothing wrong with that so long as it’s not harming others. It’s good. Good to be happy, good to help others to be happy. And Karma is just a general way of thinking about cause and effect, at least it’s one way of thinking about it. When you climb a flight of stairs and see a nice view from the top - that’s one of the effects of climbing that flight of stairs - so that is karma. In that sense we are all involved in karmic cause and effect. When you are hungry and go to the shop to buy some food - that’s you involved in karmic cause and effect too.

My example of a stair there is from Prayudh Payutto, who is amongst the most brilliant scholars in the Thai Buddhist tradition (and winner of the 1994 UNESCO prize for Peace Education), with a thorough understanding of the Therevadhan Pali Canon, who has also devoted himself to educating the public on this topic.

This is what he wrote:

There are three philosophies which are considered by Buddhism to be wrong view and which must be carefully distinguished from the teaching of kamma:

1. Pubbekatahetuvada: The belief that all happiness and suffering arise from previous kamma (Past-action determinism).
2. Issaranimmanahetuvada: The belief that all happiness and suffering are caused by the directives of a Supreme Being (Theistic determinism).
3. Ahetu-apaccayavada: The belief that all happiness and suffering are random, having no cause (Indeterminism or Accidentalism)
   
   See Misunderstandings of the Law of Kamma

There one of the biggest western urban myths about karma in Buddhism is that first one: “The belief that all happiness and suffering arise from previous kamma (Past-action determinism).” which as he says is a wrong view in Buddhism. For more on this my Karma in the Buddha's teachings

So, karma is like this ordinary cause and effect we can all see, when we walk up stairs, or go to the shops or put on a kettle for a cup of tea etc. Buddhists just take a rather broader view on it than most of us. Some of the Buddhist schools pay more attention to that broader view of karma, while others, such as Zen Buddhists, hardly pay much attention to it at all. But even with the Buddhist schools and teachers that put a fair bit of emphasis on teachings about karma, it’s not really the central teaching of Buddhism. The central teaching is much more to do with opening to others and - basically not having such a closed in claustrophobic approach to everything.

Indeed Buddha taught that you can never escape from the closed in situation we are in by this process of finding causal conditions to create nice peaceful and happy conditions for yourself. Anything that is conditioned like that is also something that can cease when the conditions for it go away. So - basically his central teaching is that the process of working with karma like that can never free you from this claustrophobic world we get caught up in, this wheel of Samsara. It can help you to have a “holiday” - a time that is somewhat more happy, relaxed, where you are not so beset with troubles that you can take a good look at what’s going on and maybe do something about it.

He taught that you can even have long periods of time with not a trace of sadness or an unhappy thought, nothing but pure happiness, or even more refined states than that, and he praised this worldly happiness.

He gives this list of four types of worldly happiness when asked by a wealthy banker Anathapindika,:

“The first happiness is to enjoy economic security or sufficient wealth acquired by just and righteous means (attki-sukha); the second is spending that wealth liberally on himself, his family, his friends and relatives, and on meritorious deeds (bhoga-sukha); the third to be free from debts (anana-sukha); the fourth happiness is to live a faultless, and a pure life without committing evil in thought, word or deed (anavajja-sukha). “

But your “holiday” will eventually end, even if somehow you could get it to last for billions of years, some ET with immensely long lives. We might meet extraterrestrials that have happy lives that will last even for a trillion years. We might feel they have everything made, that they have achieved what we are struggling to find. But according to the teaching of the Buddha, they have still not found a way out of this cycle of Samsara.

"The Buddha does not deny happiness in life when he says there is suffering. On the contrary he admits different forms of happiness, both material and spiritual, for laymen as well as for monks. In the Anguttara-nikaya, one of the five original Collections in Pali containing the Buddha's discourses, there is a list of happinesses (sukhdni), such as the happiness of family life and the happiness of the life of a recluse, the happiness of sense pleasures and the happiness of renunciation, the happiness of attachment and the happiness of detachment, physical happiness and mental happiness etc.

“But all these are included in dukkha. Even the very pure spiritual states of dhyana (recueillement or trance) attained by the practice of higher meditation, free from even a shadow of suffering in the accepted sense of the word, states which may be described as unmixed happiness, as well as the state of dhjana which is free from sensations both pleasant (sukha) and unpleasant' (dukkha) and is only pure equanimity and awareness—even these very high spiritual states are included in dukkha. In one of the suttas of the Majjhima-nikdya, (again one of the five original Collections), after praising the spiritual happiness of these dhyanas, the Buddha says that they are 'impermanent, dukkha, and subject to change' (anicca dukkha viparinamadbamma). Notice that the word dukkha is explicitly used. It is dukkha, not because there is 'suffering' in the ordinary sense of the word, but because 'whatever is impermanent is dukkha' (yad aniccam tam dukkham). "

So - working with karma does not give us a “way out”. But opening out to others and compassion and loving kindness - that’s part of the path and is a way that we can transcend all that. That’s in all the main schools of Buddhism. Along with humour and not taking ourselves too seriously, and the help of friends to bring a perspective we can’t see easily for ourselves.

It’s a path of connecting to whatever is authentic and true. Down to Earth and straightforward, and the aim is not to enter into a mystical state or a trance or anything like that.

As Walpola Rahula put it:

"It is incorrect to think that Nirvana is the natural result of the extinction of craving. Nirvana is not the result of anything. If it would be a result, then it would be an effect produced by a cause. It would be sankhata ‘produced’ and ‘conditioned’. Nirvana is neither cause nor effect. It is beyond cause and effect. Truth is not a result nor an effect. It is not produced like a mystic, spiritual, mental state, such as dhyana or samadhi. TRUTH IS. NIRVANA IS. The only thing you can do is to see it, to realize it. There is a path leading to the realization of Nirvana. But Nirvana is not the result of this path.You may get to the mountain along a path, but the mountain is not the result, not an effect of the path. You may see a light, but the light is not the result of your eyesight."

(Have just updated this with quotes from Walpola Rahula and Prayudh Payutto for the main points)