The doctrine of the three bodies is how the Mahayana holds together two things that look incompatible: that a buddha is beyond all conditions, and that a buddha walked around northern India and had a bad back.
The dharmakaya, the body of truth, is what a buddha actually is. It is not a body in any ordinary sense but the unconditioned reality itself, identified with emptiness and with the nature of mind, and it is the same for all buddhas, which is why the tradition can say that all buddhas are one at that level.
The sambhogakaya, the body of enjoyment, is the form in which a buddha appears in a pure realm to advanced practitioners, adorned with the marks, teaching without interruption. Much of the visionary and iconographic material of Mahayana and Vajrayana Buddhism describes buddhas at this level, which is why those figures are not treated as historical persons and are not thought of as inventions either.
The nirmanakaya, the body of emanation, is the form a buddha takes in an ordinary world, subject to birth, illness and death, adapted to what the beings there can receive. Shakyamuni is a nirmanakaya on this account.
Buddhahood so described is a greater attainment than that of the arhat, who is released from suffering but does not possess the full range of a buddha capacities. That comparison is the point at which the Mahayana distinguished itself, and the earlier schools did not accept the account of themselves that it implied.