Welcome to the forum.
US cave rescue organizations mostly use main and belay systems, although some may use twin tensioned systems.
Rope grabs are usually Petzl Rescucenders or 3-wrap Prusiks.
Rescue loads are usually lowered through 6-bar racks.
The belay line is usually the same 11mm static/low-stretch rope as the main line.
I've seen twin tensioned systems used in above-ground training lowering through two racks, or through two belay spools.
Here's a link to some National Cave Rescue Commission training info for students. Student Preparation Guide