Short answer... both... Ive seen ones that were obviously fitted to a specific arm.... others could be classed as generic one-size might fit all.... Officers grade holsters typically would be a higher grade of goods since it was private purchased... commonly seen fitted to a given weapon.... sometimes...
Quartermaster issued holsters such as provided to Cavalry and other mounted services.... typically would get the latter... Have seen ordnance invoices for issues of revolvers... not unusual to find allotments of different models, types and calibers in the same invoice.... at the same time issuances of saber belts... and "holsters"... without regard or mention that the respective holsters might be for one arm or another... Implied they were all issued the same general issue holster. Of course there is a wide range of styles of surviving CS holsters... much of it depended on the respective contractor supplying them at the time...