Modal verbs as Synonyms
The modal verbs SHOULD and OUGHT TO are close synonyms; WILL and WOULD are synonyms in some types of polite requests. It is sometimes difficult for language learners to choose among synonymous modal verbs. Always choose a more general synonym out of a group of synonyms or a synonym with a more straightforward meaning.
For example, MAY, MIGHT, COULD are synonyms in the meaning "possibility". MAY has two other meanings; COULD has four other meanings, two of which are rather difficult to distinguish from "possibility" without a clear context. Only MIGHT has just one meaning: possibility. The choice should be obvious – use MIGHT or MAY for "possibility".
Modal verbs as phrasal modals
Examples: be able to, be going to, be supposed to, have to, have got to, ought to, used to.
With these phrasal modals, the simple form of a verb follows to:
She's able to help us.
They are going to help us.
We are supposed to help them.