Before I forget: there was the mention of whether Black Ops is truly a Call of Duty game. By the same logic, is Bioshock Infinite truly a Bioshock game?
Call of Duty started with a number of unique features back in 2003: iron sight aiming (this was very rare in FPS games back then, as polycount was still too low for usable iron sights; the real John Mullins mentioned wanting to see it in a Soldier of Fortune game back when he was interviewed prior to SoF2's release, and America's Army was the biggest significant FPS title with it back then, unless I'm missing a few prior historical games), class-based multiplayer with TDM, CTF-style, and other objective-based modes, and a linear cinematic single-player gameplay. Black Ops still fits that rather nicely.
Bioshock had plasmids alongside weapons, and tonics to upgrade, as well as a deeper single-player storyline with NPC back stories. Back when Bioshock Infinite was revealed, there were plenty of people saying "This isn't Bioshock!", but Ken Levine said that it was, for the reasons listed above.