What constitutes a family style, from say, a more general style?

I'm assuming that a family style is just a modified version on a larger style that is passed on in that family.

So did people master numerous systems to create their own? Or use principles and techniques from one system to alter another?

It seems that if someone specializes in say, Bak Sil Lum, but changes some things while passing it on, that it would still be Bak Sil Lum, only played differently than some.

At what point does something become a "family" style?