I must admit to also having come across all these names/ideas etc, and like Mick B1 above, I long since stopped buying pre-ground tools as I invariable ended up either not using, or regrinding myself. For most of my turning, I have tended to use the tool which cuts when moving towards the headstock and thus has it's cutting edge on the left hand side of the tool, and which I know as a Right Hand Turning tool. What's in a name though?
It's worth pointing out that the RH Turning tool can be used, if canted over somewhat, as a facing tool as well. (Shock, horror, gasp etc). Hence, I can get away with a lot of my external turning with just the one tool.
I may as well point out that some years ago, I started using carbon steel tools as well, old files actually, softened, cut up, reground, and then re-hardened. Ok, they don't last long before requiring re-sharpening, but hey, the material is free, ie worn out files.
I do have a set of HSS tools hidden on a shelf somewhere, but never used. Why? Because I never seemed to need to use them given what I already have. But, I did make one mistake with this set – I bought 1/2" or 12mm square shank tools as the lathe was able to take them. A further and much bigger "but", is the amount of regrinding tools of this size take! So, don't buy the biggest tools your lathe can take: for our purposes, 1/4" or 6mm square tools are perfectly adequate – yes you will need packing to get the cutting tip at the correct height, but sharpening/re-grinding is so much easier, there being less material to remove.
I haven't really bothered about the distinction between roughing and finishing. I think it was Tubal Cain, (T.D. Walshaw) or maybe L.C. Mason who said that the average ME never uses the equipment at rates requiring a roughing tool, so I always sharpen mine as a finishing tool. I did once do some experimenting to see what the lathe could handle. Never again. The lathe was happy, but I wasn't given the amount of smoke generated by the cutting oil. So another reason for lightweight cutting.
So, there you are, my thoughts, strictly as a very amateur, amateur.
Happy turning,
Peter G. Shaw