This is a common source of confusion. So…here we go. The glass portion of the filter is 27.5mm. So we take this 27.5mm of “naked glass” and mount it in one of two ways.
The first way is to put it into a 1.25 inch filter cell. This cell has threads, so it can screw into any 1.25 inch eyepiece or screw into many filter wheels.
The second way to mount the 27.5mm of naked glass is to glue it into a 31mm metal ring. There are no threads on this ring, so it is thinner than a 1.25″ filter cell. Most people prefer this thinner profile, so long as their filter wheel accepts 31mm filters and so long as they have no plans to screw it onto a 1.25 inch eyepiece or something.
Some people call 31mm filters mounted, some call them unmounted. Call it what you wish. But we refer to them as mounted because the 27.5mm of naked glass is mounted either in a filter cell or in a filter ring. But…nobody commonly sells 27.5mm of “naked glass”. We could, if someone actually has a filter wheel that accepts 27.5mm unmounted (I sold exactly ONE that way). Yes, 36mm and 50mm filters come unmounted. But 31mm is not “truly unmounted”. You just choose between filter cell or filter ring.
More confusion comes from the fact that if you take your calipers and physically measure the diameter of the 1.25 inch filter cell and the 31mm filter ring…they will both measure 31mm.