"Not quite what you might think. Many British cartridges used a battery cup primer (Think 12ga. shotgun shell) with the battery cup serving as a rivet to hold the rim in place. The rim was a separate diac from the case."
Uhm... That wasn't really used in handgun cartridges, was it?
As far as I know, that was primarily done with the wound foil and paper cases (.577 Snider, .577-.450) in the early days before they figured out how to properly draw brass cases.
In the case of the .577 the "rim" was actually a flat iron washer. Normally there was a small brass cup at the case head that would support where the foil/paper attached to the head.
This .577-.450 shows that kind of case construction
I have never, however, heard of that type of construction being applied to handgun cartridges in the United States nor have I ever heard of the term "solid head" being used to denote a on-piece case as opposed to the built-up composite case.