Mini-essay time!
(Don't worry -- I know you hate 'em, so I'm honestly going to try to be brief.)
Regarding all the trooper variants. There are several things going on, interwoven. Evolution of the Republic/Imperial forces and their matèriel, specialist troopers, and battlefield-specific focus equipment, mainly. The core trooper is the core trooper. The Kaminoans made an army for the Republic, with armor based on the old Republic Troopers from thousands of years earlier -- the last time there'd been a standing military. That Phase I armor quickly proved not up to actual combat conditions, and many new variants were tried at the same time as attempts to improve the base kit were underway, leading through a couple transitional models to the Phase II.
I treat the stuff from the pre-ROTJ EU as tacitly in until it's not, except where it contradicts. So most of the armors from the books and games I recognize. From The Force Unleashed, I like the "Phase III" Stormtrooper armor, that has added some recognizable hallmarks of the OT Stormtroopers to the Phase II armor of ROTS, thus making the OT armor Phase IV. But even then there are variations. How much is component evolution and how much is due to different factories or better gear going to more elite units, I don't know, but can speculate. I feel the R1 version was an early Phase IV (IVa). They quickly realized the mistake of cutout tube stripes, due to that old military truism, "If there is an opening, dirt will get in it". So an idealized version of the ANH/ESB is what resulted (IVb). I see the ROTJ version as the next incremental iteration, with that "entire Legion of [the Emperor's] best troops" the first to be thus equipped (IVc).
Then there's the common mark of elite/veteran status all the way through the EU, all the way up to TFA. Black armored "shadow" versions of the main units. Troopers, Scouts, the Royal Guard... Different, better materials, advanced systems, etc. Improved sensor masking is one common hallmark. Stormtroopers have a higher level yet, the black-trimmed-with-gold Nova Troopers, who are the Stormtrooper equivalent of, basically, the President's Marine Guards.
Then there are the specialists. Pilots, armored-vehicle operators, officers, etc. I maintain everyone in the OT wearing a Stormtrooper-style faceplate was a Stormtrooper. Just as the Marines have their own pilots, not borrowed from the Navy or the Air Force. We see non-Stormtrooper armored-vehicle operators in Rebels and ROTJ. These specialists wear their outfits as standard.
...As distinct from all the environment-specific, weapon-specific, circumstance-optimized variants stocked in armories to be assigned as needed when a unit deploys to this situation or that planet. These are mostly
not daily-wear, but replace or supplement the standard loadout of whatever that trooper normally wears.
And for
all of these, the familiar terms are some of the nicknames and epithets the Rebels and the general populace use to refer to them. Proper military designations wouldn't be "Snowtrooper", for instance, but something like... "Stormtrooper Armor, Environment-optimized, Extreme Temperature, Cold". "Biker Scouts" or "Scout Troopers" are properly "Stormtrooper Scouts", and so on. So I need to see more of the role of the Mud Trooper, Range Trooper, and Patrol Trooper to come up with the actual T.O.O. niches they fill, and how much overlap or redundancy there might be with previously-established designs, but I can guarantee those are not the official Imperial designations for them.
--Jonah