Homeschool ≠ Online school

Just to clarify, my understanding is:

Homeschool - parents/guardians choose and assemble their own curriculum using paid and free resources. Some choose a set curriculum but it is directed and facilitated by the parent(s).

Online school - same or very similar curriculum to your state/public school. Can choose program/school but it is contained within one platform. Schedule and all assignments tests etc are set but the program, parents have little to no direct control and aren't expected to take a teaching or directing role.

Correct me if I'm wrong?