What is the meaning of the word "jail"?

Definitions:

A correctional institution used to detain persons who are in the lawful custody of the government. NOUN
- She was sentenced to six months in jail for her involvement in the crime.
A place of confinement for individuals accused of crimes who are awaiting trial or sentencing, or for those serving short-term sentences, usually less than one year. NOUN
- He was takent to the county jail while awaiting his court hearing.
A place of confinement overseen by local government or law enforcement agencies and is used to detain individuals who pose a security risk to society or themselves, or those unable to meet conditions for bail. NOUN
- The prison was overcrowded. so the city built a new jail to house the overflow of inmates.