From time to time, you may see posters referring to 'screwback' G-shocks with some affection!
The original DW-5xxx series of G-Shocks - the first Gs really - had a caseback design known as the screwback. This series until the DW-5600e had the same type of design.
The screwback was and is still popular on dive watches.
Basically, the original G-shock design had the module - or main body - of the watch in a stainless steel case. The back of the case was screwed on to the main body a little like a bottle top. There was a rubber gasket to help seal the back.
These are screwbacks.
Later G-shocks have modules/bodies that are made from resin/polycarbonate rather than stainless steel. Instead of the back of the watch screwing directly on to the body, the back plates are held in place by four screws - one at each corner.
On the photo attached, the right hand watch is a DW-5600c-9V and is a screwback. Note the notches around the edge of the back - these are for the tool that removes the screwback.
The left hand watch is a GW-M5600 and the back plate is held in place by the philips-head screws on each corner.
Whether screwbacks are any better is an ongoing debate! They certainly feel tougher, heavier and are generally more desirable. They're also generally made in Japan.
Models like the Frogman (with titanium instead of s/steel), the GW-5000 (with DLC - diamond like coating) and the Giez use the screwback design and are priced accordingly.
EDIT: Adam in NYC posted a thread listing screwback models. Link: List of screwback G-Shocks.