Are the transformers used in switching flyback converters regular transformers?
They're not the same.

An "ordinary" transformer never stores much energy in its magnetic field. Power entering its primary side is immediately delivered to the load on its secondary side.

A flyback transformer must build up a substantial magnetic field while current is applied to the primary, and only deliver the stored energy to the load after the primary current stops.

The requirement to store energy between the two parts of the cycle means a flyback transformer must be designed differently from an ordinary transformer. The core must be designed to store substantial energy without saturating. In the case of the application in a flyback switching converter, you'll often see them referred to as "coupled inductors" rather than "transformers" for this reason.