The exact classification of state prisons in the United States is different depending upon the county and state, but some of the common ones are as follows:

State Prison Tower
Administrative Prisons: Administrative prisons or detention centers are for very distinct purposes such as housing mentally ill offenders and the like.
Maximum Security Prisons: Maximum security prisons use a high level of external control, internal control, and supervision of inmates chiefly through the use of high security perimeters and wide-ranging use of internal physical barriers and check points
High Security Prisons: High security prisons have extensively secured perimeters, multiple/single occupant cell housing and a high staff-to-inmate ratio.
Medium Security Prisons: Medium security prisons contain inmates that may present a moderate escape risk or may pose a threat to other inmates, staff, or the orderly running of the institution.
Close Security Prisons: Close security prisons are fairly rare and typically house inmates too dangerous for Low Security, but who did not commit a crime worthy of incarceration in a Medium Security Facility.
Low Security Prisons: Low security prisons contain inmates that are not considered a serious risk to the safety of staff, inmates or to the public, and subsequently contain many rehabilitation programs.
Minimum Security Prisons: Minimum security prisons enforce the lowest level of security possible for inmates and often houses petty or “White collar” criminals.