Slaves made gladiators by purchase or court ruling (Ad ludum was condemned to the training school. Ad Gladium was to be put to the sword. It didn't matter how, and such men often fought in pairs until they died. Ad bestias means thrown to the beasts, or just as liikely, tied to a pole so the the crowd can see the ferocious beast in action) were essentially prisoners. Gladiators sold to private individuals might form personal troupes with their own premises or work as bodyguards within the house. Volunteer gladiators usually had the option to come and go.
However, it isn't always so cut and dried. Star gladiators of whatever origin might be allowed to attend functions held by important people who want them on the guest list. Sometimes a lanista might be paid for some reason to let the gladiator out of barracks (it is often suggested that lanistas prostituted their gladiators because it was known that wealthy ladies in particular sometimes indulged themselves with private liaisons. Gladiators were symbolic of virility. Scarred, ugly, it didn't matter. However, too much sex would sap the gladiators performance, which is one reason why legionaries weren't supposed to marry, so a lanista might not be too keen to do this). Sometimes a volunteer who isn't being reliable might find out what being a slave is.