Do the words "jail" and "prison" refer to different things?

In everyday speech, the terms jail and prison are used interchangeably in many situations. However, my understanding is that, at least in the US, they actually refer to slightly different things. For instance, it appears to me that it would be rather unusual for an American to use the expression federal jail. He'd most probably say federal prison instead.

Am I right? What is the correct usage of jail vs prison? Are there any (historical or legal) differences between the US and the Commonwealth?

I consider "jail" to mean a temporary, local facility where suspects are held until and during trial. In general, you can get out of jail by paying a bail bond. "Prison" is where convicted felons are sent to serve their sentence.

Thus, there aren't a lot of federal jails--there's not much point to the local and federal governments having two jails in the same city--the feds just pay the locals for use of their jails.

In the United States, jails are operated by cities and counties (or equivalent). Prisons are operated by states and the federal government. Jails are generally thought of as for short-term incarceration, such as before or during trial, or for minor crimes that result in a sentence of incarceration, usually of less than one year. Prisons are for long-term incarceration for major crimes.

However, even though there is a technical distinction in that every one of these institutions will have a name which is usually one or the other, jail is a generic term that can refer to prisons or any type of “correctional facility”.