Just to add, if you use microtonal music, then often C# will differ in pitch from Db and C## may also differ in pitch from D. For instance in 31 equal, a commonly used tuning that’s a kind of extended quarter comma meantone with very pure major thirds, the sharps and flats go like this: C, Dbb, C#, Db, C##, D, …

You still get enharmonic equivalences, now it’s E## = Gbb and C###= Ebb etc.

In extended pythagorean tuning, and other just intonation tunings, or tunings based on an infinite lattice of intervals, then they may never join up.

The pattern can get very complex if you use a tuning with the fifth tempered to sharper than the 700 cents of twelve equal as then for instance Db becomes flatter than C#.

C … Db .. C# … D …

This for instance is the pattern you get for 53 equal, a popular microtonal tuning which is a slightly tempered extended pythagorean tuning.

Also, now you have to go up to four sharps or flats for enharmonic equivalence. E.g. D#### = Bbbbb and E#### = Cbbb

For more on this, see Robert Walker's answer to To be totally unconventional, should a piano with keys of E# and B# be produced? Would it be more versatile and more interesting?