Fair enough - if who I replied called it, "prison", I'll remit my nit-picking ;)
But usually you cannot bail out of prison, right? You get arrested, and go to a city jail, where you can get bailed out. If you are found guilty, you go to county or prison to serve a sentence.
The terms are fairly interchangeable. There's no hard and fast rule or law that states "jail" is one type of incarceration and "prison" is another. In the U.S., we lean to referring to long-term incarceration as prison and short-term as jail, but that's a fairly "local" thing.
But to what you're thinking of, I believe that is correct; bail is for short-term incarceration pending a trial. If you've been tried and sentenced, you can't bail.
But usually you cannot bail out of prison, right? You get arrested, and go to a city jail, where you can get bailed out. If you are found guilty, you go to county or prison to serve a sentence.