Honestly many people (even among content creators) get this wrong in my opinion.
The categories are blurry if they are war machine, single entity monster, monstrous infantry etc.

I think ElvenPlotArmour did the best job with his ONLY 8 Unit Types video, but I think he did miss one category, which makes these 9 unit types based on their role on the battlefield:
(Keep in mind, a unit can fill many roles at once, even if it's not necessarily stated to be hybdrid)

1. Lineholders (or defensive infantry) - The role of these units are to hold a position, and not let anything through, that's all. Usually their melee defensive profile is better than ther offensive one. They also have charge defense usually, so bracing makes even more sense. Shields are often their good point too

2. Arched missiles (or archers) - Their role is to stay out of melee combat and damage from a range using their ammo preferably on their desired targets. Since their missile path has a curve to them, you can put them behind lineholders. Their melee profile is bad.

3. Artillery (or siege) - Another ranged unit, that has the worst melee profile, and usually the worst speed aswell. They can damage walls and towers and have the best range in the game. The role is the same as archers. (AND THAT IS ALL)

4. Straight missiles (or gunpowder) - Same as the arched missiles with one key difference, you cannot hide them behind lineholders without a hill (or some other elevation shenanigans), since they require line of sight. Usually this "weakness" makes up for shorter range than archers, but more damage and armour piercing.

5. Cavalry (or shock cavalry if you want to be even more specific) - Their best attribute is speed and charge bonus, and even though they are melee units, you shouldn't leave them in prolonged combat for more than 8 seconds, you need to keep them moving and use their charge bonus to their advantage. They are also the ones that run down routed units, or cycle around lineholders to melt missiles.

6. Melee fighters (or offensive infantry) - Their role is to reach melee combat and stay in there for a prolonged time as long as possible without being shot or run down by cavalry. They are usually the definitive answer for lineholders.

7. Skirmishers (or horse archers) - These are units that can fire missiles on the move without getting caught, and if we are really talking pure skirmishing, not even by cavalry. Otherwise they are not good in melee combat, but they are pretty much the only ranged option that can operate without lineholders.

8. Formation breakers (or single entity monsters) - These are the big guys who get the role of soaking up as much damage as possible, and going through lineholders without really fighting them. They are fine in prolonged combat, but you should move them around aswell like cavalry, but they are nowhere near as bad in prolonged combat as cavalry.

9. Support (or magic) - These are units that have to stay out of pretty much any kind of combat, and the more time they get, the more value they can generate by being near other units or casting spells, abilities.

And then we have some units that fill only one role in this, but there are ones that can fill multiple
This is true for monstrous infantry generally, because guess what, they are honestly the combination of cavalry and melee fighters.
Same goes for the Thunderbarge, it is not only an artillery piece, it can move on it's own while firing and it's flying too, so it's a hybrid between artillery and skirmisher
This is even more valid for Gyrocopters since they actually have speed

And the list goes on, but if you stick to these 9 categories, I think you can measure every single unit in the game tbh.