The latter. The bottom slides forward in a U-channel on either side and the back drops down, at least on the sideways mounted couches. On some newer SMB's they added in drawer slides for the bottom instead of the U-channel but it wasn't an improvement IMO.
On the '50' style couches facing forwards, at least some of them have a hinge like most VWs, futons, etc. where you pull the bottom up and towards you and the back scoops down in an arc and drops into place.
I don't have one to show you at the moment but someone probably does.