Auto-clamped handles in action
Note how as the handles of the selected keyframe approach gradually taper off as they approach the neighbouring keyframe instead of "overshooting" (i.e. pushing the curve past the neighbouring extremes).
Perhaps the most irritating/confusing of those quirks though was that "auto clamped" handles were a weird mixture of standard "auto" handles and a per-curve setting. While all the other handle types were per handle, this per-curve setting really threw things a bit.
As of a commit last night, these are now per-keyframe settings. As can been seen in the screenshot below:
As can be seen, Auto-Clamped handles always stay horizontal when their keyframe defines an extrema, while with plain Auto handles, your handles can end up tilted and/or going in all sorts of crazy directions.
What's common about both though, is that the horizontal length of the handles varies depending on the horizontal distance between a keyframe and the surrounding ones.
Hopefully this visual guide to the variants of auto-handles currently available in Blender has helped you understand the differences between these.
Certainly as a result of working on this, I now have a better appreciation for the different types of handles, and also have a better (excuse the pun) handle on how the handle calculation stuff works. Previously I'd avoided touching this stuff, as it was kind of black magic which, if tinkered with in the wrong ways would break animation files. However, I found that this modification was not only possible, but relatively simple and straightforward to do too!