there are a lot of flyback transformer driver schematics. many of them have 2 transistors that switch a primary winding. ive heard them referred to as half bridge and some reffered to as push pull. i believe the two attachments are an example of each.
A halfbridge usually has two switches and two capacitors to maintain a middle voltage between the positive and negative of the DC- bus. So what you posted is a halfbridge. The transformer works with one primary winding.
A push-pull usually has two windings on the primary, so polarity is switched by energizing the two windings alternately.