"Can" is definite: He "can" go to school. Whereas "could" is only a possibility: He "could" go to school.
They are both model verbs indicating that something may/might happen. "May" is a possibility indicating that something could happen: May we go to school. But "may" can also be used to affirm something: You may go to school. "May" can be used in a few other ways too. Whereas "might," also similar, has different sub-uses: With considerable might he picked up the school house. It can also be used as a possibility: might we go to school; or, we might go to school. It can also be used to indicate that somebody should have done something: You might have told me he picked up the school.
Sorry I don't have time to answer the other two. I'll check back later to make sure somebody else answered them all.
Sounds like something you could probably just ask the overmind. Wikipedia has a pretty good discussion of auxiliary verbs here en.wikipedia.org/wiki/Auxiliary_verb, though you will have to search a bit more for a full explanation of all of the items on your list.
Home / Grammar, Usage / The difference between: can/could, may/might, will/would, that/which
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