Why are there different versions of this character?

We see three Jay Garricks Hunter Zolomons:

• Earth-1 Hunter - in the park. This is the one that "Jay" and Caitlin watch. He has no active involvement in the plot. Much like communism, he's just a red herring.
• Earth-2 Zoom/Hunter-Prime (surviving). This is the one still currently alive, who just acquired more of the Speed force.
• Earth-2 Zoom/Hunter-Remnant (dead). This is the one that Zoom killed in front of everyone.

Like the Reverse-Flash, Zoom needed Barry to run faster, for the intended goal of stealing his improved abilities. For Thawne, it was to go to back to the future; for Zolomon, it appears to be able to cure whatever sickness is killing him.

Zoom-Prime was able to convince Zoom-Remnant to die so that Zoom, as an entity may live. Why would Zoom-Remnant agree to this? He's not exactly sane. He's spent some undetermined time going through daily shock therapy, and has become detached from feeling any remorse or guilt.

Barry: And you just don't care how many lives you destroy trying to get it? How many people you kill?

Zoom-Prime: No, I don't! That feeling was taken from me a long time ago.

Like the Reverse-Flash, both Earth-2 Zooms understood that the key to their survival was the long game. Zoom-Prime explains to Team-Flash that he needed to be in two places at the same time to be able to convince everyone that he was on their side. It's a brutal plan, for sure, but one that a murderous dying psychopath is willing to agree to.

Similar discussion about The Prestige (spoiler warning): Why would Robert Angier use the machine every time?