A lot of the confusion comes from the difference between the counter system in vanilla and the expansions. The counter system of vanilla is explained first.
There are two parts to the counter system: damage multipliers and plain old unit statistics.
All units have tags that define what types they are (a unit can be more than one type), and some units have damage multipliers for specific types which either increase or decrease their damage against that type of unit, depending on whether the multiplier is larger or smaller than 1. For example, hussars are of the type "heavy cavalry" and pikemen have a multiplier of 5 against heavy cavalry, which means that instead of doing their normal 8 damage, they do 40 damage (8 * 5 = 40) against hussars. Knowing the types and multipliers of each unit is very important, and it is fortunately a lot easier than memorizing them one by one. More on this later.
All units have a cost, and the cost-efficiency of the units also plays a large part in the counter system. Some units sacrifice statistics for other benefits, such as high multipliers, which makes them more specialized units and worse all round units. Two contrasting units in this regard are hussars and skirmishers. Skirmishers are extremely good at what they specialize in—killing heavy infantry and light cavalry—due to their long range, high ranged attack with high multipliers, and ranged resistance. However, they sacrifice melee damage, melee resistance, and hitpoints, which make hussars a strong counter to skirmishers despite hussars not having any multipliers at all. Some units are simply very cost-inefficient even against the type of unit they are supposed to counter, and if that unit is an exceptionally cost-efficient one they may outright win that fight. An example of this is crossbowmen against janissaries.
Lastly, on the topic of unit statistics, there are three types of damage: ranged, melee, and siege. All units have either ranged resistance or melee resistance, and this is represented by a number between 0 and 1 which reduces damage taken of that type by a percentage 100 times the number (e.g. ranged resistance of 0.30 reduces ranged damage taken by 30%). Note that there is no siege resistance.
Fortunately units of the same type generally share the same purpose, which means that there is no need to memorize all of the multipliers. There are four main types of units:
- Heavy cavalry: commonly referred to as "hand cavalry". This unit type generally has high speed, hitpoints, and damage, but with no multipliers and no ranged attack. This unit type is generally an all round good unit, which means that it is generally strong against any unit that is not specifically designed to counter it.
Strong against: light infantry, artillery
Examples: hussar, cossack
Light cavalry: commonly referred to as "ranged cavalry". This unit type generally has high speed and high ranged damage, especially against heavy cavalry. This unit type generally specializes in killing heavy cavalry.
Strong against: heavy cavalry
Examples: dragoon, cavalry archer
Heavy infantry: This unit type generally has a melee damage multiplier against all cavalry, but naturally has trouble getting into melee combat against light cavalry. This unit generally also has high siege damage.
Strong against: heavy cavalry, buildings
Examples: pikeman, musketeer
Light infantry: This unit type generally has a long range attack with multipliers against heavy infantry and light cavalry.
Strong against: heavy infantry, light cavalry
Examples: skirmisher, cassador
Note that there is no multiplier for light infantry in vanilla. This means that there is no need for units such as skirmishers and cassadors to have this additional tag; just the type "infantry" is sufficient. Since the game developers wanted to introduce a new type of infantry to the game, they decided to remove the "light infantry" tag from skirmisher-type units, and give it to their new category of infantry. Units such as the skirmisher and cassador that were light infantry in vanilla are now—by convention—referred to as "ranged infantry", which is unfortunate since there is a "ranged infantry" tag refers to all infantry with ranged attacks, including units such as musketeers. You can however disregard this in-game "ranged infantry" tag as its only purpose is for an uncommon upgrade that you get from Zen temples. Whenever someone says "ranged infantry" they are referring to skirmisher-type, crossbow-type, or longbow-type units.
The unit type that was introduced in The Warchiefs is infantry that plays the role of heavy cavalry, now called light infantry. These units play the same role as heavy cavalry and are almost countered the same way. Heavy infantry does have a high multiplier against light infantry, albeit significantly lower than the one against heavy cavalry, but light cavalry doesn't. Light cavalry instead has a multiplier against specific light infantry-units, but not all of them! Examples of light infantry are coyote runners and tiger claws. The term "light infantry" is appropriate because they clearly don't wear heavy armor since they can run so quickly.
This is the only difference between vanilla and the expansions regarding the counter system. What was known as light infantry before is now simply nothing but infantry but commonly referred to as "ranged infantry", and a new unit type has been introduced that is of the type "light infantry".
Although the type of the unit very often correlates with their role in the counter system, there are plenty of exceptions. Not all heavy cavalry-units are strong against skirmishers, and not all heavy infantry-units are strong against heavy cavalry. Here's a list of some notable units:
- Rifle rider: This unit is tagged as both heavy cavalry and light cavalry which means that it is weak to both light cavalry (since they counter heavy cavalry) and ranged infantry (since they counter light cavalry). This unit has a very quick ranged, albeit short, attack with high multipliers against both heavy cavalry and heavy infantry.
Urumi swordsman: This unit is tagged as infantry only, just as skirmisher-type units, their main purpose is to counter heavy infantry, also similar to skirmisher-type units, and they have a ranged attack just as skirmisher-type units do. However, they have a range of 2, meaning that they need to be in melee range to do their ranged damage, and they have an area attack. Their ranged resistance is also through the roof.
Rattan shield: This unit is tagged as light infantry and plays the part of heavy cavalry as one would expect. However, light cavalry has no multiplier against rattan shields, making them very hard to counter.
Cuirassier: This unit is a normal heavy cavalry-unit, but with incredible statistics and an area attack. The area attack is very strong against clustered enemies, which happens naturally when armies are large, especially if the enemy units are small. For this reason cuirassiers fare very well against pikemen and musketeers despite supposedly being countered by them. I'll admit that the cuirassier is included in this list partly due to personal bias.
Now I need to submit this post, so I'm hitting that button.