Is this true ?
Is most research based on CP in the home ?
Most recent research (by recent I mean, since the 1970s) is. Prior to that, there was quite a lot of research into corporal punishment in schools, a lot of which is still relevant, and which is the best available research because of the relative dearth of more recent research.
Does research into CP at home, differentiate between reasonable CP from loving parents, and the excesses of beatings and abuse?
Normally, yes.