Ok here's a complete (I hope) list of underfeatures you can have in DF 31.03
1: Magma pipe, which starts from the magma sea and piereces all the way up to one of the three cavern layers, most commonly to layers 2 and 3 . If it pierces all the way to the surface it digivolves into a volcano.
2: Underground lakes, which can be limited or connected to the corner of the map. Connected lakes refill as time passes, while limited ones can obviously be drained.
3: Chasms, which are round like hollow magma pipes that connect two cavern layers or more. They don't have bottomless tiles in their bottom so they make poor dump zones. A magma pipe can also continue above the magma level as a chasm. Chasms don't seem to ever breach into the surface.
4: Demonic fortress: A slade tower that goes all the way from hell to the middle cavern layer, it has an adamantine weapon in the floor somewhere in the middle, which if removed opens the glowing floor beside it unleashing hell upon you. Its upper (demon free) layers are usually filled with undead friends.
5: Paths to lower levels, that are discrete one tile ramps that connect layers 1 and 2 or 2 and 3.
6: Caves, which are similar to the 40d caves, have a megbeast inside usually and often filled with loot around. They also are passages to cavern layer 1
For Z-layer thickness, it seems toady used an average volume system for making caverns. If you have the passage worldgen parameter set at 0-100% and openess at 0-0 you get very tall caverns made of spaghetti-like bendy passages, which can span anything from 5 to 20 layers or more. If you set openess to 0-100% and passages to 0-0% you get very wide spreading flat caverns that span at most some 6z levels, but don't have the annoying spaghetti-passages. It seems the total volume of a cavern section made of passages or openess is the same, but open caverns are flatter since they have less "noise" from the passages. The total thickness of your underground relies on the cavern height span. Worlds made of 0-100% openess caverns and no passages (0-0%) are quite flat and average 30 to 50 z levels between surface and the magma ocean (and beyond). Default DF worlds have an average of 120 to 150 (way more in some unusual sites) Z levels between surface and the magma ocean.