For most of the last two centuries the Second Buddhist Council was told as the moment Buddhism broke in two. The account ran that the monks of Vesali, defeated over the ten points, walked out and formed the Mahasanghika, the great assembly, leaving the Sthaviras, the elders, behind; and that every later school descends from one side or the other of that room.
The Vinaya account does not say this. It closes with the ten points settled, the offending monks corrected, and the community intact. The schism appears in different material altogether, later and separate, and it turns on a quite different question: five theses about the limitations of the arhat, the perfected person, which one party held and the other rejected. Nothing in the earliest layer joins the two events.
Charles Prebish set the problem out plainly in a survey of the scholarship, and the position that has since become ordinary is that the two should be kept apart. There was a disciplinary quarrel at Vesali. There was a schism, somewhere afterwards, over what an arhat is. Tradition welded them together because a single dramatic rupture is easier to hold in mind than a slow divergence, and nineteenth century scholarship inherited the weld without inspecting it.
This matters beyond the detail. Buddhism's early history is often narrated as a sequence of councils, each producing a decision and a split, and that shape comes largely from later chronicles with their own reasons for wanting a clean line of descent. Taking the join out of Vesali leaves a messier picture and a more honest one.