I've heard several terms for this little sub-set of holds, but not all of them were the original Japanese name. All of these are based around one of the fundamental hold downs of osaekomi waza (pinning techniques), kesa gatame, or "scarf hold".
The first, most basic form can also be called hon kesa gatame (hon meaning "main" or "basic/normal/regular"). Oddly enough, I had a hard time finding a decent picture of it online (everyone seems to favor one of the variations).
Then there's what I've mostly heard of as the "envelope" but which is technically kuzure kase gatame. I most often hear kuzure translated as "broken" but most online dictionaries translate it as "crumbling" or "collapsing", which makes me wonder if this hold was originally thought of as a lesser form of the hold, as in "the world is falling apart and this is the best hold you can manage"? Hmm. Anyway, here's what it looks like, mostly like kese gatame, but with your right arm around uke's middle rather than the head.
There's also ushiro kesa gatame (ushiro meaning "behind" or "rear"). For a long time I mistakenly called this one kuzure, thinking kuzure meant something like "reverse". Oops. Here, you're facing uke's feet.
Lastly, there's makura kesa gatame. I'd never actually heard a name for this and had to do some research. I've always heard it referred to simply as the "pillow hold" or "pillow lock" (because uke's head is sort of "resting" on your thigh). I thought maybe that was a quaint western nickname for something whose name they either couldn't remember of just didn't know. Turns out makura actually translates as "pillow." Oops again.
There, now I've got myself straightened out and I can sound like I know what I'm talking about!