What is the difference between prison and county correctional facility?

There are several major and minor differences.

First, they are both lock-ups. While most prisons are state run, some are privately run, and there are several Federal facilities around the country. Inmates in the prison setting have all been convicted and sentenced to usually a year or more (often more), and County inmates serve less than a year. Many county inmates are people who have not been able to make bail or bond and are awaiting trial, but some have been sentenced. Many people will say that County inmates have committed much less serious crimes, but this is not the case. Usually, it means they have less of a record or had a better attorney who was able to bargain a lesser sentence.

The time is served in a different manner too. County time is usually spent in a cell with two or more "cellies." Penitentiary time can be served in a cell, a room, or in what is called dormitory fashion (sounds sort of pleasant, doesn't it?). County time is done with little access if any to the outside, while Pen time usually means "yard time" that can last anywhere from an hour a day (or several times per week) to open yard times except for after nightfall and during count-times.

There are a number of minor differences that change from facility to facility also.