There are four different endings in the campaign in Call of Duty: Black Ops 2.
The ending you see is based solely on the outcomes of the major turning points in the game, like whether Woods dies or not, how much Intel you found, etc.
There are some major spoilers here, so I wouldn’t suggest reading through these on your first playthrough.
Pyrrhic Victory – Rescue Woods
Celerium – Recover the Celerium Worm
Old Wounds – Interrogate Kravchenko to learn about the CIA mole
Time And Fate – Collect all the intel to learn about the CIA mole
Fallen Angel – Find Zhao’s secret meeting intel / Harper’s protected
Karma – Save Karma / DeFalco dies
Suffer With Me – Menendez is not able to manipulate Woods
Achilles’ Veil – Keep Farid alive / SDC allies with US military forces
Odysseus – Save Admiral Briggs / SDC protects the USS Obama with Drones / USS Obama survives long enough for SDC reinforcements / Karma and the USS Obama survive the attack
Cordis Die – Rescue the President
Judgement Day – Capture Menendez
Pyrrhic Victory – Rescue Woods
Celerium – Recover the Celerium Worm
Old Wounds – Kill Kravchenko without resistance
Time And Fate – Find intel; thoroughly search the compound
Fallen Angel – Find Zhao’s secret meeting intel / Harper’s face is burned
Karma – Karma dies
Suffer With Me – Menendez is able to manipulate Woods / Woods dies / SDC left vulnerable
Achilles’ Veil – Attempt to shoot Menendez / Farid dies
Odysseus – Admiral Briggs dies / USS Obama has no defenses to counter assault / USS Obama’s crew killed
Cordis Die – Rescue the President
Judgment Day – Capture Menendez
Pyrrhic Victory – Rescue Woods
Celerium – Recover the Celerium Worm
Old Wounds – Kill Kravchenko without resistance
Time And Fate – Find intel; thoroughly search the compound
Fallen Angel – Find Zhao’s secret meeting intel / Harper’s face is burned
Karma – Karma dies
Suffer With Me – Menendez is able to manipulate Woods / Woods dies / SDC left vulnerable
Achilles’ Veil – Attempt to shoot Menendez / Farid dies
Odysseus – Admiral Briggs dies / USS Obama has no defenses to counter assault / USS Obama’s crew killed
Cordis Die – Rescue the President
Judgment Day – Kill Menendez
Pyrrhic Victory – Woods dies
Celerium – Recover the Celerium Worm
Old Wounds – Kill Kravchenko without resistance
Time And Fate – Thoroughly search the compound
Fallen Angel – Find Zhao’s secret meeting intel / Harper’s face is burned
Karma – Karma dies
Suffer With Me – Menendez is able to manipulate Woods / SDC left vulnerable
Achilles’ Veil – Save Faird / Attempt to shoot Menendez
Odysseus – Admiral Briggs dies / USS Obama has no defenses to counter assault / USS Obama’s crew killed
Cordis Die – Rescue the President
Judgment Day – Kill Menendez