9001/9002/9003 were basically B7G reworks of Acorns, yes. The Acorn had leadout-sealing issues and so by the early-1940s when WWII-requirements for millions of B7G-based valves for things like the BC1000 [WS31] military radios and RADAR stuff emerged in the US it made sense to re-engineer the old Acorn electrode-structures to fit the newer, more-reliable/cheaper-to-produce envelope.
The 6AK5 is my favourite from that era: Small, compact, reliable... what's not to like.
[There was an interesting diversion - the likes of the 717A -
http://www.r-type.org/exhib/aab0012.htm and the 387A -
https://www.radiomuseum.org/tubes/tube_387a_we.html - which were electrode-assemblies really rather like the Acorns but fitted into old-style Octal bases. Long lead-outs made these really not worth pursuing above about 40MHz]