Note: spoilers for Spectre ahead!

In Spectre, we meet Franz Oberhauser (Christoph Waltz). He later reveals he now goes by the name "Ernst Blofeld", and has a scar just like the original Blofeld. But he also states he took the name "from his mother's side".

My question is, is Oberhauser a descendent of the original Blofeld (from On Her Majesty's Secret Service among others), or is he supposed to be the same Blofeld character?

I know the Daniel Craig series of Bond films are a reboot/prequel of sorts. Is Spectre showing the "genesis" of the character?