Not sure if generalized plasmid taxonomy is going to be relevant any longer. A lot of these old names were created before the exact sequence and function of the various DNA sequences were known. This is becoming especially true as synthetic biology allows us to mix and match parts of plasmids at will. If you want to dig through a lot of the old plasmid classification papers, a lot of them are published before 1980.
Back then I'd imagine conversations went more: "oh look, I found an R plasmid conferring ampicillin resistance", instead our more modern understanding: "oh, I have a plasmid conferring ampR via bla "
That being said, I think the more specific / specialized plasmid classifications will stick around for a while as they confer a lot of domain specific meaning. Check out Ti and Ri plamids which have very specific meanings in plant pathogens and are used in the genetic engineering of them. You'll notice that the classification for these plasmids comes from a lot more than a single gene.
There have been some modern attempts to classify plasmids, but rely a lot more on the structure / lineage of the plasmid rather than the payload genes (replication origin, size, etc.). Check out  for an example.
 Wang, et. al. 2009. Plasmid.