Black Ops Cold War's campaign is one of the most immersive campaign playthroughs you will ever experience. Before you proceed, note that the content below contains major spoilers. If you haven't already, we highly recommend you complete the campaign and experience it yourself first.
There are two main endings in Black Ops Cold War. You can get either one of them depending on the answer you give to Adler during a dialogue prompt in the mission "Identity Crisis." Once you find out that the CIA has brainwashed you, Adler will ask you about Perseus' whereabouts.
This dialogue prompt triggers a chain of events leading to either a "good" ending or the "bad" ending.
You can either choose to tell the truth or "lie" to Adler.
If you decide to tell the truth, you will get a mission called "The Final Countdown," where you will join Adler and the rest of the CIA team to sabotage Perseus' plan to launch the Greenlight Nuke all over Europe.
After successfully stopping Perseus, you join Adler on a cliff overlooking the Solovetsky Islands. You two exchange a series of dialogues where Adler explains that whatever he did to you was for the "greater good" and that nothing was personal.
Adler then asks you to make one more "sacrifice" and you both pull guns out on each other. Shots are fired, after which the game ends, followed by the ending credits. Since the screen goes to black, it is unclear who got shot.
If you lie to Adler, you will trigger a new mission called "Ashes to Ashes." Once you're done talking to Adler at the CIA safe house you will have the option to inform Perseus about the team going there and help them set up an ambush at Duga (the location where the mission "Ashes to Ashes" takes place).
When you and the team arrive at Duga, they suspect you of lying and confront you. Upon confrontation, you have the option to signal the Russians to attack the team. You are then tasked to kill Mason, Woods, Adler, and either Lazar or Park, depending on who you saved in the earlier mission called "End of the Line." You heard it right. You kill the main Black Ops characters. Hence the reason it is called the "bad" ending.
You then re-unite with Perseus to go inside the building to finish off the wounded Adler. The mission ends after you order the Greenlight nukes to go off all over Europe.
Bad Ending (Alternate Version)
There is also a slightly altered version of the bad ending with the same outcome but different events. After you lie to Adler at the CIA safe house, do not set up an ambush at Duga. Then, once you arrive at the location and are confronted by the team, you are immediately killed by Adler on the spot.
The mission ends here with the same outcome as the original "bad" ending, with the Greenlight nukes going off, but the main characters remain alive.