The thing is, there are two kinds of radiation from the sun. Fast moving particles, which cause the solar storms, and the photons from the sunlight.

Mars gets about half the amount of sunlight Earth does. Even with an Earth atmosphere, it would not be warm enough for trees to grow there at the equator without extra help such as planet scale thin film mirrors in space, or industrial levels of production of greenhouse gases (cubic kilometers of material needing to be mined every century to make the gases).

On the Mars surface you get much more UV light than on Earth where most of it is absorbed in the ozone layer.  But other levels of light are much less.

SOLAR STORMS AND COSMIC RADIATION ON MARS

Mars gets much more radiation from solar storms as well as cosmic radiation. It's atmosphere is so thin that it doesn't provide much protection.

Levels of cosmic radiation on the Mars surface are similar to the ISS, and astronauts can only spend a couple of years or so total on the ISS before they run out of their lifetime limit of radiation exposure according to the guidelines for exposure in radiation environments. It may also depend on whether they fly during solar minimum or solar maximum. The details depend on the age of the astronaut and their sex, as men and women are affected differently in the States. In ESA and Russia then women and men have the same maximum doses.

I can't seem to find a table of how many years typically it is for astronauts of various ages and sexes, though I'm sure I've seen one somewhere. Will update this if I find one - or do say in comments if you know where to find it.

But techy details here:

http://prediccs.sr.unh.edu/paper...

The ISS orbits within the Earth's magnetic field so is protected from the worst effects of solar storms. Those can be extremely high levels of radiation. An astronaut unprotected in deep space or on Mars could die if exposed to a solar storm for a few hours unless they got immediate emergency intensive hospital care. So solar storm shelters are essential for any deep space exploration.

You would be protected from solar storms in a cave such as have been found on both Moon and Mars. Or by covering your habitat with several meters of "soil" (regolith, rocks "gardened" by meteorites over billions of years into a soil like consistency).

We are protected from cosmic radiation by the ten tons per square meter Earth's atmosphere. They are hardly deflected by the Earth's magnetic field at all, magnetic fields provide no protection from them. But they are constant in flux, you don't get "galactic storms" like the solar storms. Many of the particles still get through as you can see in a cloud chamber, particles traveling at close to the speed of light. But human bodies are adapted to tolerate that low level of radiation so they are no problem for us.

So the reason Mars has more cosmic radiation and more radiation from solar storms is because it has almost no magnetic field to protect from solar storms and almost no atmosphere to protect from cosmic radiation and give additional protection from solar storms.