As an avid D&D player, I do see that while the overall concept of the game remains the same across all editions, there is a great deal of difference among the editions, enough to warrant singling each out as a different game.
Notably the following:
D&D, 1974-1977, aka "Original D&D" or OD&D
D&D Basic Set, 1978-1980, aka "Bluebook" or "Holmes" D&D
Advanced Dungeons & Dragons, 1978-1983, aka 1st Edition AD&D or AD&D 1e
Basic D&D and Expert D&D, 1981-1982, aka "Moldvay/Cook D&D" or B/X (they are NOT separate editions as the poll makes them, just separate sets, one expanding the other.)
D&D Basic, Expert, Companion, Master, and Immortals sets, 1983-1991, aka "Mentzer D&D" or BECMI. Also includes the D&D Rules Cyclopedia compilation, 1991-1997? (Not sure of end publication date). For the most part this is a continuation of B/X, though there are a few minor additions and clarifications/changes to B/X, as well as more detailed rules for levels above 8th, including the ability of the PCs to eventually become and act as "gods."
Advanced Dungeons & Dragons 2nd Edition, or 2e. Significant changes from 1e.
From 1992 on there was another set called "D&D Classic" or "The New Easy to Learn D&D", or "Black Box D&D" (for the color of the first printing's box), which was pretty much just Mentzer all over again, but with an emphasis on using a pre-made board as the shell for dungeon maps and cardstock printed standees, placing a mild emphasis on miniatures again. Along with this was a little known boxed set aimed at younger players call "Dragon Quest" (not to be confused with the SPI game Dragonquest, which is a different beast). It's pretty much the same game, but offers simplified approaches using cards to represent spells, equipment, treasure and magic items, not unlike MB/GW's HeroQuest game.
And then Wizards of the Coast buys out TSR (1997) and Hasbro buys out Wizards (1999) and we get:
2000-2008: D&D "3rd edition," aka WotC D&D, or 3e/3.5e. The "Advanced" label was dropped, and the rules were altered considerably, with some bits from all the previous games slipping into the mix. Confusingly, it's not the 3rd edition of anything; WotC simply used that as the logical progression from "2nd Edition AD&D." The "3.5e" came from revisions to deal with complaints arising from complications the 3rd edition introduced.
2008-2014: D&D "4th edition"— aka 4e— is a major departure from any other edition, placing an emphasis on tactical play and incorporating ideas from video game RPGs into the mix. Generally despised, though it has some fans for that tactical emphasis. A commercial flop, which prompted WotC being fully brought into Hasbro as a division of the company, and provoked a review and overhaul of the D&D system, producing…
2014- present: D&D "5th edition"— aka 5e— aka D&D Next (though that was essentially a "beta" release). A simplification of ideas introduced in 3/3.5e and to some extend a return to some original styles of play, this is the current edition. It does play differently from previous editions, with its own specific and unique rules.
And then there are the various "d20" third party systems licensed for the mechanics of 3/3.5e and the "Old School Renaissance" or OSR third party "retro clones" which seek to replicate (and occasionally alter or "improve" or even combine) the various TSR editions.
Are all of these "D&D"? Yes. Are they all the same, and is the experience of playing them all the same? No.
It comes down to this: If you're really interested in RPGs and D&D in particularly, they are most definitely not the same game. If you're only tangentially interested in RPGs and specifically D&D, then they are the same game. The differences are like comparing American College Football to NFL Football to Canadian Football to "touch" Football to Flag Football. Yes, they're all the same game, but no, they're not the same game.
A proper break down is probably:
Original D&D
Holmes Basic D&D (it really is its own beast, though it's an "introduction" to both OD&D and AD&D 1e!)
AD&D 1e
"Classic" D&D (B/X, BECMI, RC, "Black Box")
AD&D 2e
D&D 3e/3.5e/d20
D&D 4e
D&D 5e
These encapsulate not only significant rules differences but also significant differences in styles of play.