Yes, King was the parent company. Although for some reason not all Regulas carried the King branding.
The company occupies a rather strange place in German camera history. Surviving the mass die off of companies in the early 70s, only to be killed in the 80s by an investment in a bad technology (disc film!!!).
One of the odd things about their 70s cameras is that they're fitted with ISCO lenses. ISCO pulled out of the SLR lens market in the early 1970s, and seemingly, excepting Regula, the rest of the camera lens market as well. Even the Regula SLR ended up using Japanese lenses. But for whatever reason (maybe an old contract?) ISCO continued to supply Regula's fixed lens cameras through the 1970s.
In the 80s they mostly sold 110 cameras, some of which were of rather nice quality by 110 camera standards (meters and bright line viewfinders - wow!).