As another who went through a frenzy of saw-making for about a decade or so, I did a lot of reading & searching around the topic. What I found about naming conventions for backed saws is that they vary from country to country & over time. Here in Aus., just about any saw with a spine will be called "tenon saw" by the majority of woodworkers of all degrees of skill. Some distinguish, but their terms rarely match those of someone else, completely. I've suggested in an article I wrote for a local mag on choosing & using small saws that we adopt the term "backsaws" as used in North America, as a general name (whether it originated there or not, I don't know, but they have certainly popularised it over he last 40 years or more).
I started with 'western' saws more than 60 years ago & am so rusted on to that style of cutting I would find it extremely difficult to change to pull saws. In fact I did try them back in the 70's when all tools Japanese were suddenly the rage, but we didn't get on at all, & I didn't persevere. I envy the ambidextrous types who can switch seamlessly from one to t'other, but I'm definitely not one. Either type can do the job, so if you are just entering the arcane world of hand saws, begin with whichever appeals to you and stick with it 'til you can saw well.
To distinguish between saws, I think it's far more useful to specify size & tooth pitch, not what you may or may not cut with it. I would once have said that hang-angle is equally important, and it sort of is, but different people like different angles for doing the same tasks; so much depends on bench-height, how you secure the workpiece, & simple personal preference.
Again, the choice of size of saw, tooth pitch & configuration (x-cut or rip) matter, but individual choices vary so widely. What you start with & learn to use has a huge influence on how you view saws.
About the only guidelines I give anyone who asks me these days is to find saws you are comfortable with, keep them sharp & well-set, and use them 'til they become part of your anatomy. Of course there are rules of thumb like having at least 4 or 5 teeth supported in the cut, but the height & length of the saw is your choice (I do advise using a length that gives you a comfortable stroke). Ease & comfort of use generally translates into efficient & accurate sawing.
Set is a source for endless argument. The problem is it depends not only on the wood, but he skill of the sawyer. I've watched beginners fight with one of my saws that were perfect for the job in hand (or so I thought! ). Not only the hardness, but the typical MC of the woods you work with will have a big influence on your preference. Down our way, our dry, hard woods need far less set than you'd use cutting softwoods at a higher MC, for e.g. My advice here is to figure out the minimum set that gives you free-cutting and a little bit of 'steerage'.
If you are lucky & pick up a saw of any type that is sharp & well-set and suited to you & the task in hand it'll be love at first sight, & you'll be hard to persuade that any other saw could possibly be as good!
Cheers,
