Remington used the REM-UMC headstamp (and Peters used PETERS) until the early 1960s, when they went to R-P. As the old headstamp bunters wore out they were replaced with the new R-P ones, so some calibers may have used the REM-UMC headstamps longer. Sort of the same timing when Winchester and Western went to W-W headstamp.

Regarding the foregoing discussion about "balloon head" what many today call balloon head are what the factories called "solid head." What happened was that the very earliest inside-primed cartridges were all made of thin brass or copper sheet. When the factories changed to the use of Boxer primers, the case construction was changed to the solid head (which the manufacturers usually abbreviated as "SH"), which was fairly shallow with a protruding primer pocket. Later the solid head base was made thicker, like the ones in use today. That became a necessity for most CF smokeless powder rifle loads. Those provide a reduced case capacity vs. the earlier solid head case style but are stronger and better able to withstand higher pressures. The early SH cases are perfectly safe to use when reloading standard velocity handgun loads if you happen to have any. But as they are all fairly old and may show cracking, corrosion, etc., they should be carefully inspected first.