Another word for your list is "popper"....which is another word that's come to the fore of my experience since Grover's birth. BrE popper is the equivalent of AmE snap, which is to say it's the name for a type of fastener, as illustrated to the right (image from madeinchina.com). Searching for this photo on the web, I found that a lot of dealers in such fasteners call them snap buttons, but to me they're just snaps. The OED, in its definitions for snap and popper, calls them press studs. This counts as a baby-related word since one is constantly doing and undoing snaps/poppers at the crotches of (BrE) babygros/(AmE) onesies in order to get at (BrE) nappies/(AmE) diapers. I don't know why, but I feel silly saying popper, so I've been glad that I seem to be able to get away with snap. (Better Half won't let me get away with diaper, however.)
When one fastens/unfastens snaps, one snaps [and unsnaps--see comments] them, so I just asked Better Half what one does to poppers. He says you pop them. To my AmE ears, though, it would sound funny to pop something closed--things pop open, but don't pop shut. But perhaps BrE ears don't have that bias. [Added 29 Jan: The difference seems to be that snapping involves making a closure, and popping usually involves undoing the fastening. I'm pretty sure that no one says unpop to mean 'to fasten a popper'. So what seems to have (AmE colloquial) weirded me out here is that the verb doesn't seem to describe fastening--the purpose of the device--but describes unfastening. Both dialects' words are onomatopoetic.] (Your thoughts?)
(For other BrE/AmE differences in the use of the word snap, see here.)
Another clothing fastener that differs transatlantically is (BrE) zip versus (AmE) zipper. (The verb in both varieties is zip.) One is tempted to form the theory that there is a strict economy of syllables: dialects are allowed a fixed number, and since press studs have two syllables in BrE and one in AmE, some other clothing fastener had to inexplicably differ in its number of syllables. It would be a silly theory, of course, but it appeals to my taste for symmetry.
When zips/zippers are at the front of a pair of (BrE) trousers/(AmE) pants, they mysteriously differ in their number: in BrE you must take care to do up your flies, while in AmE, you do up your fly. But that matter is discussed in the comments for this old post, so please see there for more details.
I can't think of any more clothing fasteners with dialectal differences...but I'm sure someone will point them out if they exist...