Pretty much, as I understand it.
Oh, there are print differences, of course.
The original
B2 was written to accommodate the Basic D&D Holmes rules (the "blue book") and went out with the second issuing of that set as I remember. When the '81 Moldvay edit rules came out, the
B2 was revamped to jibe with the changes within that manual; though some of the changes were,
IMO, more esoteric than actually needed.
But I will yield the floor to any that have more intimate knowledge on the matter.