The 1st image does not appear to be a classic flap, it looks like a seasonal bag. Classic flaps are definitely made super puffy at times but this doesn't look like one and the strap length looks too long. Maybe ask the seller for more info. or check the interior hologram code to see what year it's from.
The beige bag is a single flap and can be called a single flap or a Diana. Although it doesn't share the Diana shape you are used to seeing they were both made in/around the same time and this one is an earlier version. So Diana version 1.0 and the other is Diana version 2.0