I thought I understood wiggle and local wiggle, but my ideas didn't match what I found on the wiki pages.
After some chatting with Susume, alwen, and Formula350, I finally did a little testing. (As Susume pointed out, "wiggle is determinate".)
The big surprise was local wiggle. In the original interface, when you right-click (or control-click) and select "Wiggle" from the wheel menu, you get local wiggle. If you click on a sheet, it local wiggles the sheet and any adjacent loop sections. The wiki had the local wiggle part correct (although not super-clear).
In the selection interface, if you double-click on the same sheet, it selects the sheet and adjacent loops. But when you wiggle, you get global wiggle. Even though it's wiggling the same segments, global wiggle produces move points early on. (I tested using the starting pose for puzzle 1354, where there are lots of points to be gained.) You can't do a manual local wiggle in the selection interface.
The good news is that recipes work the same way in both interfaces (as you would hope). Also, using structure.LocalWiggleSelected produced the same results as a manual local wiggle from the wheel menu, provided the segments selected and the number of iterations are the same.
One tricky part is what happens if you right-click on a loop and select wiggle. This gives you local wiggle of the loop, the adjacent helixes or sheets, and the loop adjacent to the helixes and sheets. So generally, a lot more segments will be affected when you wiggle a loop in the original interface.
The wiki pages had some of this right, but were a little misleading on other parts of it. I've started to make some updates.
These the v2 function references have been updated and expanded:
"Further Research Is Need."