my transformer has a secondary winding of 0 - 12v - 24v
Is it just labelled differently and is it really a center tap where 12v would be the center, 0 would be -12v and 24 would be 12v?
Not necessarily. If the transformer is rated to produce full output from either the 12V tap or the 24V tap, it could be that the winding from the 12 to 24V terminals is of a finer gage, since the current that could be drawn from the 24V tap would be half that you could draw at 12V. This you can determine by comparing the resistance of the 0-12 and 12-24 windings.
Would that matter for using it as a center-tapped +/- 12V transformer? Not much, the terminal voltage at the high side would be fractionally lower under load, but the overall heating compared to drawing the full power at a single tap would actually be less.
I would guess that yes, it is just a regular center tap transformer. Assuming that's the case:
The outputs will be AC, so -12V doesn't really have any meaning. The 12V here will be 12V AC, and the 24 will be 24V AC.
If you make the center tap 0, then "LABEL 0" will be 12V, and "LABEL 24" will also be 12V (but they will be out of phase with each other).
Based on the labeling, I think it's fairly certain that this is a regular transformer, but I would do some continuity tests just to make sure.
0V is arbitrary as it is floating secondary centre-tapped coil.
so you can relabel with 3 choices;
0 : 12Vac : 24Vac 12Vac : 0V : 12Vac +180 deg 24Vac : 12Vac : 0V