All planes on the ground (mostly MiG-29s, and MiG-21s at the end) have Hungarian ensigns (red-white-green triangle) and different paintworks used by different Hungarian units.
The aircraft used by Col. Banning and Capt. Holiday change on different occasions throughout the movie. For example, we see Col. Banning in a dog-fight sitting in his F-16 but after his landing he steps out from a Russian-made MiG-29.