My own D&D taxonomy, which I'll admit is limited and heavily biased.
OD&D: The
fons et origo of them all, and so loose a toolkit that all others can be said to descend from it.
Advanced D&D 1st Edition: The first stream of descent from OD&D, emphasizing expansion of the original game along with strong structure, codification and uniformity of basic systems across all games, and with a range from gritty low fantasy to epic high fantasy, although often tinged with amorality and ruthlessness.

The systems start to focus around careful development, mechanical individualization, and balance over a character's or campaign's lifetime.
AD&D 2nd Edition: A descendant of and sidestep from 1E, with a bit more openness and considerably less grittiness.
D&D 3rd Edition: The penultimate expression of the AD&D "A Rule for Everything" sub-paradigm (cf. comments by Peter Adkison and Jonathan Tweet,
Thirty Years of Adventure, pp. 257-258), with a deliberate return to 1E in many respects, both in flavor and in the desire for mechanical individualization of characters and standardization of rules across games, although mechanics cover considerably more space than they did in 1E, and balance moves less from a campaign scale to a level scale.
D&D 3.5: The
ultimate expression of the aforementioned paradigm, although the standardization started to fail as the designers pushed the boundaries of the system.
Basic D&D: The second stream of descent from OD&D, distinguished at first for legal reasons, but serving as the expression of the looser side of the OD&D philosophy. Very much a game of loosely structured, free-wheeling high fantasy fun and adventure using mechanically archetypal characters, with very little worry about mechanical standardization beyond the basics.
Fourth Edition: The third stream, taking from everything that has come before but with the strongest influences from 3.5 in mechanics and BECMI in spirit, High fantasy adventure with a rigorous, standardized, uniform and transparent combat structure and a looser non-combat structure, focused on strong archetypes that contain high degrees of mechanical individualization within them and on giving every character the opportunity to shine in an encounter or adventure.
(A lot of this is drawn from the observations of others about the D&D family, especially Lawrence Schick's Heroic Worlds and Roger Moore's "The highs and lows of fantasy" in DRAGON #163.)