>>863840I'll answer in the most non-assholish way I can.
Climbers typically use dynamic rope with stretch, so that if you fall your spine doesn't snap in half, and cavers use static rope because you typically aren't climbing up and down the wall when on rope and that makes it better for the specific technique they use, which I'll get into later.
Harnesses, in caving, have a butt loop so you can sit in it while on the rope. As for what's on your harness, cavers carry cowstails (carabiners on a short length of rope for doing change overs in case you need to go the other way on the rope), a rack with a hyperbar (for descents), and a chest and hand ascender (jumar) with a foot loop (for ascents). All of the caving gear doesn't require someone on the other end of the rope keeping friction, like in climbing. You just tie off on an anchor and go.
Descending on a cave requires that you run the rope through the rack, tie it off properly, and then use your hand to guide it through going as fast or as slow as you want on the rope. Ascending is harder. You put the hand ascender above the chest ascender on the rope, stick your feet in the loop attached to the hand ascender and then you sit in your harness. Move the hand ascender up as far as you can go and then stand up. Sit again and move the hand ascender again. Keep going till you're at the top. This specific method is called "the frog method."
Ascending without the assistance of the rock in climbing is called "jugging" and requires two jumars with a webbing ladder attached. It's a really awkward motion, at least for me.
The two are pretty different in comparison to technique (cavers tend to use their knees more to climb) and gear. Some knots carry over and the idea behind anchors is very similar, but they're really two different beasts. Especially when in the cave and having to crawl around and through tight spots.
