No, infect deals damage in the form of poison counters. So it adds 2 poison counters, but removes 0 life.
On creatures, it's not the same. Blocking/attacking only deals damage (which is temporary) to their defense. Infect is more powerful because not only is it more permanent, but it also weakens their power too.
Proliferate is to take any number of creatures and/or players, and add a counter to them of a type already there. So if a player has a poison counter, you can add another. If a creature has a -1/-1, +2/+1/ etc. counter on it, you can add another, and you can do this to everything on the battlefield and all players. Moving counters is to take a counter that's on one player or permanent and basically remove them from spot A and put them on spot B. Both spot A and spot B must be legal targets for the counter of the targeted type.