Although many native English speakers use these two terms interchangeably, there are differences in terms of (1) individuals who are held, and (2) who has jurisdiction over the respective institutions. (1) Jail Persons held: People awaiting trial; people sentenced for a short duration, typically less than a year. Not normally used in UK. Jurisdiction: In the United States - Run by the county sheriff's department. In Canada, run by provincial governments. (2) Prison Persons held: People convicted of crimes; sentenced for a longer term Jurisdiction: In the United States - Run by the Prisons and Corrections office in the respective states. There are also federal prisons. In Canada, run by the federal government (also called Penitentiaries).

A jail is a place that temporarily holds people who are awaiting trials. A prison is a place that holds convicted felons for long periods of time.

jail is for small crime but prison is for big crime

Grant's answer is correct for the US. Most of the time people use the two words interchangeably, though, and many people don't know the difference between the two words.