Foot-in-the-door starts small: get someone to agree to a tiny, easy request, and they become measurably more likely to agree to a larger related request later, because agreeing to the first one shifts their self-image toward 'the kind of person who helps with this.' The classic 1966 study by Freedman and Fraser found homeowners who'd agreed to display a small window sign were far more likely to later agree to a large, unattractive yard sign than homeowners approached cold.
Door-in-the-face works in the opposite direction: open with a deliberately large request you expect to be refused, then follow with a smaller 'compromise' request — which is actually the request you wanted all along. The refusal creates a sense of reciprocal concession ('they backed down, so I should too'), making the real ask land more easily than if it had been the opening move. Both tactics exploit a consistency drive rather than the actual merits of the request, which is why noticing which one is being used on you — and evaluating the final ask entirely on its own terms — defuses both equally well.