All those turned BY the pure-blod are not pure because they were not born as a vamp, therefore they are Thin-bloods
I am not saying that, I am the one who said those turned by pure bloods are are half-blooded (second gens). I think you're reading the wrong posts because I never said pure bloods can make pure-bloods.
Whoever Molag turns, is pure-blooded and then they have their own bloodline which gets diluted, Volkihars had harkon and his family as the progenitors, Order vampires have their own. As does every single clan out there.