There is Original D&D, a three book boxed set from 1974 with supplemements I-IV (Greyhawk, Blackmoor, Eldritch Wizardry, and Gods, Demigods, and Heroes). That is generally referred to as OD&D. O for origninal or 0 for 0e as preceding 1e.
In 1977 there was the Holmes Basic Set with a blue box and red dragon cover art. It was a precursor to 1e covering slightly different rules from Oe. Five point alignment for example was new.
1e 1977-79 came out with the 1e MM, PH, and DMG and used a bunch of OD&D rules with the rules from the supplements and Holmes Basic and its own stuff. 1e established nine point alignment for example.
1981 you had the Tom Moldvay B/X basic set (B/X stands for the Moldvay Basic and Dave Cook Expert sets from 1981) which was a distinct rules system with different stat modifiers, race as class, and going back to OD&D 3 point alignment.
1983 Had the Frank Mentzer BECMI basic set rules (Basic, Expert, Companion, Master, Immortals sets) which were basically B/X with tiny differences and higher level add ons.
Later there was the Rules Cyclopedia basically compiling BECMI except for the immortals set into one book.
Then the Black box basic rules which covered BECMI levels 1-5.
So 1981 B/X basic on is basically one compatible line of interchangeable basic rules repackaging and what most refer to as Basic D&D.
OD&D is an earlier D&D system with distinct rules about as different from later basic as 1e is. Some call the Basic D&D line OD&D but that leads to a lot of confusion.