This is a confusing relationship, but there are a few important differences between the programs:
All Sloan-Kettering labs are open to Weill Cornell students, but Cornell labs are NOT open to Sloan students.
The other main differences are in the programs' structures and curricula. Cornell's is a larger program and has standard length rotations (semester). Sloan is a small program (~10 students) and has 3 week rotations, which is very unusual. Sloan has one "Core" course, which is separated from the rotations in time and is completed during the first year. Cornell's curriculum is more rigorous, and it is a more traditional program.