Terminology is important.
Moreover, it is important that the definition be determined by who holds ultimate authority. If the parent holds the ultimate authority they are homeschooling...if another entity holds the authoriy they are doing not. Keep in mind, I am not saying the parent has lost their complete authority in the home. They have just decided to allow another entity to hold the authority for the education of their children.
A distinction is necessary to ensure that the freedom to homeschool is not lost through increased regulation. If we combine the two groups then when the state seeks to increase regulation on the "schooling at home" crowd the "homeschooling" crowd could be affected by the changes and potentially lose some of the authority to direct the education of their children.
Here's an article that sums it up pretty well.
The foundation of the original fight for homeschooling was freedom. Many virtual academies and cyber charter schools begin with leniency, but over the years,A distinction is important, not to cast judgement, but to keep clarity in who is affected by increased regulation. That's a distinction all should welcome because if the parent ever decides to abandon the cyber or charter school for another way, they will have the freedom to do so without having to prove anything to the state.
rules creep in, subtle new policies begin to crop up, and gradual restrictions choke out your choices at home like crab grass run amok. This sets a precedent to increase regulations on other students who are educated at home, whether they're enrolled in a virtual academy or not.