BECMI D&D took center stage in the TSR universe with the publication of the red Basic box set in 1983. The Basic Dungeons and Dragons box set was followed up by the Expert, Companion, Masters, and Immortals box sets. Thus the name BECMI D&D. However, it took decades before people started referring to that series of box sets as BECMI. Those of us that played it at the time simply referred to it as D&D, as opposed to the unnecessarily complex AD&D.
TSR ended its support of BECMI D&D in or around 1994-1995, with the end of its support for Mystara (the BECMI realm) in 1995. During that time, many rulebooks, adventures (modules), and supplements were published. Also, three magazines (Dragon, Polyhedron, and Dungeon) occasionally featured articles or adventures for BECMI D&D under the name of “D&D”.
Adventures and articles for AD&D could also be adapted for D&D. It took some guess work to do the conversions. Most of us players and dungeon masters of D&D would not take on the effort to convert AD&D to D&D.
Most players of BECMI D&D adopted the adventures and supplements from the older BX D&D and even older original D&D. We mostly considered BX D&D to be the same game as our favored D&D, just slightly outdated. So many Basic and Expert D&D modules and supplements from 1981 and before were adopted by BECMI D&D enthusiasts. Commonly, you’d see BX rulebooks at the same table as BECMI rulebooks during sessions. No one thought that was strange.