Your pictures show normal, one strap holsters... the strap goes over the weapon and snaps to the thumb break. That was the normal way holsters worked until the rotating hood style was invented back in the nineties, and it's still quite common. Especially since they don't cost a hundred and fifety bucks...
Rick uses that holster throughout most of the show... except for a few scenes where he's got an old two-strap one. The two-strap holsters have two dangly straps that snap together over the weapon, and when they're unsnapped, they both flop down to the sides... they were really tough to re-snap with only one hand, too.
With the kind in the pictures, the thumb snap part, which is against the body, is rigid (usually due to steel reinforcing) and doesn't flop around at all. You can re-snap it with one hand, something that countless cadets had to do many pushups over until they got it right...