The original Basic (the 'Holmes Blue Book' by J. Eric Holmes) was actually a reorganization and simplification of OD&D, not Advanced D&D (despite Holmes being published around the same time as AD&D). Holmes was intended as an introduction to OD&D; AD&D was extensively revised from OD&D, and the OD&D/Holmes rules were very different from AD&D in many ways.

There were at least two more revisions of 'Basic', which was updated into the early 1990s. It was much more a separate game, not a lead-in into 'Advanced', and I think publishing it may have been a contractual obligation to D&D's co-creator, Dave Arneson, who was gone before AD&D.