There are probably small differences in meaning, but they basically express the same idea. You can use them almost interchangeably. "Apparent" is probably more common, but speaking as an American, I experience both words as the same.

Thank you

Don't worry about the difference because there is not much.

If you like to tie words together, I'd say to think of it like this. Evident means that we have evidence that this is true. We know it to be real, or we at least have facts that show that we feel certain something is going to happen. Whereas apparent can be tied to apparently. Meaning more like "It seems, it appears." More emotion based than fact based.

The difference between them as adjectives is that evident is obviously true by simple observation while apparent is capable of being seen, or easily seen.