I was feeling like going through my library, I made a list of what I think best fits the criteria of what OP meant, but again, hes right, they dont make a lot of these anymore, I'm just listing them cause I'm bored mostly hehe.
FPS: The Darkness 1+2, Singularity, TimeShift , Prey (2006), Riddick, Syndicate (2012), Far Cry 1, FEAR, Clive Barker's Jericho, Darkwatch, TimeSplitters, Painkiller, Legendary, Duke Nukem, Rainbow Six: Vegas 1+2, James Bond Nightfire/GoldenEye Reloaded/Agent Under Fire, Resistance 1-3, Killzone 1-3, Bulletstorm, Urban Chaos - Riot Response, Hard Reset, Judge Dredd, SW - Republic Commando, Star Trek - Elite Force, Chrome, Section 8, Unreal II - The Awakening, Mace Griffin Bounty Hunter, Alien vs Predator, Turok, Area 51, Darkest of Days, Soldier of Fortune etc
TPS: Binary Domain, Vanquish, Inversion, Fracture, FUSE, Army of Two, Max Payne, The Punisher, Dead To Rights, Eat Lead - The Return of Matt Hazard, Dark Sector, Wanted - Weapons of Fate, Kane and Lynch, Spec Ops - The Line, Stranglehold, Wet, Red Faction - Armageddon, James Bond - Everything or Nothing, NeverDead, Syphon Filter, 50 Cent - Blood On the Sand, Jason Bourne (2008), Mission Impossible - Operation Surma, Alpha Protocol, Splinter Cell (especially stuff like Conviction), Quantum Theory, Shadows of the Damned, Lost Planet 1-3, Avatar (2009), Front Mission Evolved, The Bureau XCOM Declassified etc
Basically AAA or AA shooters with a 6-10h campaign that you could finish in 1 day or over a weekend. Maybe they had some multiplayer mode, but it could be ignored. These types of games are a dying breed. Yes we are still getting them, but if you want to see the difference, just go to wikipedia, sort shooters by year of release and get depressed.