No, it's not synonymous. If you precommit, you become a cooperator, but you can also be one without precommiting. If you are an AI that is written to be a cooperator, you'll be one. If you decide to act as a cooperator, you may be one. Being a cooperator is relatively easy. Being a cooperator and successfully signating that you are one, without precommitment, is in practice much harder. And a related problem, if you are a cooperator, you have to recognize a signal that the other person is a cooperator also, which may be too hard if he hasn't precommited.
but you can also be one without precommiting
What? The implication goes both ways. If you're a cooperator (in your terms), then you're precommitted to cooperating (in classical terms). Maybe you misunderstand the word "precommitment"? It doesn't necessarily imply that some natural power forces the other guy to believe you.
I spoke yesterday of the epistemic prisoner's dilemma, and JGWeissman wrote:
To which I said:
And lo, JGWeissman saved me a lot of writing when he replied thus:
I make one small modification. You and your creationist friend are actually not that concerned about money, being distracted by the massive meteor about to strike the earth from an unknown direction. Fortunately, Omega is promising to protect limited portions of the globe, based on your decisions (I think you've all seen enough PDs that I can leave the numbers as an excercise).
It is this then which I call the true epistemic prisoner's dilemma. If I tell you a story about two doctors, even if I tell you to put yourself in the shoes of one, and not the other, it is easy for you to take yourself outside them, see the symmetry and say "the doctors should cooperate". I hope I have now broken some of that emotional symmetry.
As Omega lead the creationist to the other room, you would (I know I certainly would) make a convulsive effort to convince him of the truth of evolution. Despite every pointless, futile argument you've ever had in an IRC room or a YouTube thread, you would struggle desperately, calling out every half-remembered fragment of Dawkins or Sagan you could muster, in hope that just before the door shut, the creationist would hold it open and say "You're right, I was wrong. You defect, I'll cooperate -- let's save the world together."
But of course, you would fail. And the door would shut, and you would grit your teeth, and curse 2000 years of screamingly bad epistemic hygiene, and weep bitterly for the people who might die in a few hours because of your counterpart's ignorance. And then -- I hope -- you would cooperate.