To me, D&D means, at a minimum, Vancian spellcasting, the core races, and the four arch-core classes (fighter/fighting-man, wizard/magic-user, cleric and rogue/thief). Now, it doesn't have to use those names and it can excise bits and pieces - although it's worth noting that, with the exception of halflings in Dragonlance and, IIRC, gnomes in Basic/RC and Dark Sun, *none* of the officially published settings or versions of D&D since AD&D 1e have dropped even a single one of these elements. Even settings as outlandish as Dark Sun had basically the whole set of races and classes. Oh, and paladins got dropped from DS and Dragonlance, too.
In contrast to d20 fantasy, it also specifically means using the 3.5 or 3.0 core rules and/or the SRD as its basis, with everything in them assumed to be 'on' by default unless it's listed as an optional rule.
d20 fantasy, on the other hand, implies (to me) dropping significant portions of the D&D sacred cows, be it the class structure, the core races, Vancian spellcasting, etc. Perhaps more importantly, it implies getting to this point by outright using a different core book, be it Arcana Evolved (essentially 100% compatible but stand-along) or d20 Modern (probably 80% compatible and also standalone). d20 Modern is probably the 'default' for what I would call d20 fantasy over D&D and using it cements that it's the former rather than the latter. Alternately, Grim Tales.
I very much prefer what I call d20 fantasy, since it's better at modelling the kind of fantasy I like (broadly, either Sword & Sorcery in the Howardian tradition or anime/JRPG-style fantasy ala Final Fantasy, rather than epic/high fantasy in the Tolkienesque tradition).