By the eve of Leon Trotsky’s death in August 1940, the American Trotskyist organisation, which was by far the most important group in the Fourth International, had split. Two currents of Trotskyism had begun the process of complete separation, but only begun.
It would take most of a decade before the evolution of two distinct species was complete.
For brevity they can be named after their chief proponents, James P Cannon and Max Shachtman. Trotsky’s political relationship to those two currents is one of the things that will concern us here.