It depends on the context and sentence structure (many uses...). But: Can I have a coffee? = neutral May I have a coffee? = polite (asking permission). When I was young, older people sometimes said something like this: ME: Can I have some more cake? AUNT (etc): You can, but you may not! (In other words: I know you are capable of eating more cake, but I am not going to give you permission to do so...)

here are some links that helps explain the uses of may and can. https://en.oxforddictionaries.com/usage/can-or-may https://dictionary.cambridge.org/grammar/british-grammar/can-could-or-may

You can use the times you want to use the other, because you may have more use options: In the question, MORE is more formal than CAN: Exemplo: May I go to the bathroom? (formal) Can I go to the bathroom? (Normal or informal) And it also has the "modal verb" form, which indicates the probability of something happening, and when you use CAN, you mean that there is a very high possibility of that happening (around 90% chance), and the MAY you say that there is a 50% chance of that happening.I Can go to the Gym I Can drink beer (90%) I May drink beer (50%) Bye!