These words are often used interchangeably, but they have different meanings.
Can refers to objective possibility or capacity. For example:
- Can you jump over that chair?
- I can edit this document in one hour
- I can go to that party on the weekend
- Can there be more debt-free Greeks in Melbourne than in Greece?
May is used in situations involving choice, chance, uncertainty or permission.
- There may be more debt-free Greeks in Melbourne than in Greece (but there may not)
- I may be able to edit this document in one hour (I’m not sure if I can)
- May I go to that party on the weekend? (i..e, will you allow me to go?)
- You may be able to jump over that chair (but I doubt it)
Usage of can and may has changed substantially in recent decades. People in polite society would once have asked “May I have this dance?” My children ask “Can I go to Stella’s/Emi’s sleepover on Saturday night?”, when really they should say ‘may’, but this usage, though polite and grammatically correct, is now very old-fashioned. Nevertheless, in my view at least, there remains a difference between can and may when it comes to table manners. Strictly speaking, “Can you pass me the salt?” is a question of capacity to pass the salt. “May I have the salt?” is better; after all, you already know there’s salt available, and you’re pretty sure your fellow diner can pass it to you – it’s just a polite way of getting someone else to do something for you.