I believe that was 2e.
IIRC Arneson was getting royalties on the 1e MM and they had a legal fight that he won about the 1e MMII with the ruling mostly focusing about the name so we got the 2e Monstrous Compendiums which he did not get royalties for.
No, that was definitely 1st edition. Gygax lost the court case so he ended up having to pay royalties, but a lot of the rationale for creating AD&D and D&D as separate lines was to restrict Arneson's royalties to D&D proper.
There was no need for a separate AD&D game, and indeed, Holmes version of basic suggested a transition from those rules, directly to the Players Handbook. Under Cook and Moldvay and later, Mentzer, a separate line was created.