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!