The double-figure-8 is pretty rare in climbing, it's the regular figure-8 loop that's used. Sometimes called a "figure-8 follow-through" to describe the tying method. The "double-figure-8" has two loops, it's not at all commonly used in climbing. Mostly just for some improvised rescue situations as part of an improvised harness to replace a damaged harness's leg loops.

yup, it's also great for fixing and equalizing a rope to a sport anchor for top rope soloing, etc. https://www.alpinesavvy.com/blog/fixing-a-rope-two-knots-to-.... Super easy to adjust/equalize.

Yep, you're totally right. I had double and triple on the brain from the Fisherman's; standard climbing knot is but a simple figure-8.