Theravada is the oldest form still around.

Three important main ones is that in theravada, post enlightenment buddhas only retain form for a short while. After that the enter paranirvana and no longer have a causal relationship to anything in reality. The goal of those in theravada is just to likewise enter paranirvana. In mahayana, this is considered a lower goal. The higher goal is to stay in the world helping others get enlightened. And buddhas often stay in their own realms and incarnate repeatedly or bring you there. For this reason mahayana is much more likely to believe that everyone will get enlightened eventually.

A second important distinction is that the concept of emptiness is expanded. Theravada points out that distinct objects and composites are empty. Implying that what exists are just the parts in perpetual flowingness. Mahayana expands this by saying that even the pieces are empty of distinct existence.

The third is the dharmakaya. Theravada describes very little about what happens when you enter paranirvana. It only describes it by what its not. Like negative theology. Mahayana expands this into a kind of abstract... its not a thing, but an underlying reality. And is the true reality that in a sense "is" what buddhas become. Note that point #2 and 3 are not necessarily incompatible with what theravada believes per say, but rather expand on it. There are other things, but those are some major ones.

Vajrayana is a bit harder to place, since some consider it to just be part of mahayana. It is like mahayana, but often tries to expand it in esoteric ways, and tries to create special practices for liberation that is closer than the far off ones others hope for. It also sometimes believes in something called an adibuddha which is the closest there is to a monotheistic god in buddhism. Its kind of a collective group mind of all buddhas, but in reverse is the fundamental reality that all buddhas are by virtue of enlightenment. Vajrayana talks about esoteric things like underlying ability to tap into and channel buddhas.