Should be fairly easy to see if it is screwed on or glued. Remove the toilet (sounds like you already have) then remove the wood screws holding the flange to the wood.
There is a tool made for removing the flange, but in case you don't have one of those handy: if you tap on the flange in a counterclockwise direction gently with a rubber mallet and something small enough to fit in the rounded slots, but rigid (a large bolt?) it should move without too much force applied.
Of course, there's always a chance that it's glued, in which this method might either break the glue or the flange. In any event, if it is glued you would have had to break one or the other to get it out.
My flange screws in, FWIW. I imagine your original tank did too, and it doesn't sound like it has been changed out...
A wild guess: the wood may be over the floor because the original plywood rotted out?
The only way to really know that is to rip up the wood (assuming it doesn't just have screws for removal) or remove the belly and black tank.
How about a buncha photos...?