I don't mean clone in theme, but clone in basically based on the same engine, and sharing many similarities in system and features. All three spoof various works of other genres in hidden easter eggs or certain levels. All three have wisecracking one liner speaking characters, etc. The gameplay is all pretty much virtually the same.
All three had cutscenes at various points (although I think for 3D Realms two games it was mostly at the end of each act).
Basically all three of these games (is Redneck Rampage included?) took the same engine, and just slapped different artwork on the backgrounds textures and enemies. But the functionality, physics, and interactivity was about the same. Story told mainly through manual, and occasional cutscenes?
Blood 2 sounds different, and more in line with the more modern FP-game era. At least in that mid-era when things like Half-Life, System Shock, Deus Ex were being released. But I guess Blood 2 is still simplified down to the basics (certainly none of the System Shock 2 or Deus Ex rpgs elements)?
From what I've seen of Painkiller it seems like it was designed to be a return to the more simple era of FPS from that early Wolfenstein/Doom/Rise of the Triad era. It also has cutscenes at various points as I understand it? But not much really to do with a storyline within the levels themselves.
I would contrast those pure action games (less story), with Dark Forces which was also from around that early era. Ya, also SCIFI themed (more like Duke Nukem), while it didn't have any neutral NPCs. It at least added an interesting dynamic with the character's comments were very storyline specific (he didn't say much unless it was something important to say, and described the situation, not unlike Garret in the Thief games or Patrick Galloway), and he often said things to important enemies (like when he encounters Boba Fett), or discussed things with Jan Ors his co-pilot (calling her in to bring the ship, get information, or update her on what he had found). Such that the plot was more 'integrated' even into the levels themselves (it also one of the first games to have proper story based mission objectives within the levels). It moved away from the earlier standards of keycard hunting. The cutscenes between levels and mission briefings were pretty well written. All giving the illusion of a more living breathing world.
On a side note, another game for people who like Blood, and early FPS era, is Hugo's Nightmare 3D. It didn't have much of a story like previous Hugo adventure games. But it did play off the haunted mansion theme pretty well. Zombies, ghosts, vampires, etc. Ya its from that era that the limits to puzzles was pretty much key hunting and buttons... Don't even think it had any mission objectives.
http://en.wikipedia.org/wiki/Nitemare_3D