Hello Bionika: I am not familiar enough with protocols and procedures involving "inmates". You are discussing a penal or prison system, right? The phrases have very similar meanings, with little to no discernible differences, as far as I can tell. A "deprivation of liberty" is used to show that some freedom is being denied to a person who is ordinarily entitled to certain freedoms in their daily routine. A "restraint of liberty" ...ditto, ditto, and so forth. I have no specific knowledge that one phrase is preferred over another. .

I've never heard 'restraint of liberty'. You restrain the prisoners, thereby depriving them of their liberty.