Whether you need to reapply depends on where your inmate is moving from and to, and the distinction matters practically.
If your inmate moves within the same state correctional system, your visitor approval generally stays valid across facilities in that system. In Mississippi specifically, if your paperwork is on file with the Mississippi Department of Corrections and your inmate transfers from one MDOC facility to another, that approval travels with them. You do not need to start the process over every time they move within the state system.
The situation changes completely when your inmate moves from one system to another. If they were in a county jail and just got sentenced and transferred to an MDOC state prison, your county-level visitor approval does not carry over. You need to submit a new visitor application through the Mississippi Department of Corrections process to be approved at the state level. County jails and state prisons run independent approval systems that do not communicate with each other.
The same principle applies across state lines. An approval in one state is not recognized in another state's system. If your inmate was transferred from another state into the Mississippi DOC, any prior approval from that other state means nothing in Mississippi and a fresh application is required.
On why someone gets moved to the Mississippi State Prison, it simply means they were convicted of a state crime and sentenced to serve their time in the MDOC system. The state determines the appropriate custody level and facility based on the nature of the offense, sentence length, and classification factors. It is a standard sentencing outcome for state-level felony convictions.