The second bike is not a true folder, it's more like a hybrid of a folder and a mini-velo. This is an older Pacific Reach. It rides pretty much like a normal bike (at least so far as I remember what a normal bike feels like). There's front and rear suspension and a built-in rear rack.
You can pack this bike inside a suitcase by removing the front wheel and swinging the rear triangle under so that the rear wheel rests inside the fork. But it's not practical to fold it and carry it around like most folding bikes.
I'd love a new version of this. They've upgraded it with disc brakes and some other nice things, but I think you now have to import them from Asia and it's absurdly expensive.