Disclaimer: I know for gameplay reasons blahblahblah. This is only for run.
1. Pike
Not only in AOE. In many other games pikes are considered (1) weapons for lower-level grunts (2) inferior to halberds (3) only good against cavalry (4) popular throughout the middle ages. None of them is correct. Most “pikemen” units in most games never used actual pikes but some other sorts of polearms, or merely short spears.
AOE2 pikemen are early, lower tier halberdiers carrying a glaive.
AOE3 pikemen do use pike but have the poorest melee stats among melee units (musketeers included).
AOE1 is probably the only game that does pikes justice, and it is assigned to…a Roman centurion carrying a large scutum shield which is a combination that likely never happened.
2. Arquebus
Arquebus falls in the awkward position of being (perceived as) too late for a medieval game and too early for an early modern game (from an Eurocentric view which the games inevitably have).
In AOE2 there is no arquebus, only a technology that buffs the hand cannoneer. Janissary also carries a hand cannons. Even in very late battles like Kyoto or Lepanto, you still have hand cannons. The conquistador model in DE are probably the only unit with something that resembles an arquebus, or a blunderbuss.
In AOE3 maybe because in late 17th Europe the traditional “ranged” gunpowder unit evolved into all-purpose line infantry, a change cannot be reflected by the game mechanics. So European civs start with musketeers with bayonet. What should have been the arquebusier’s role, a weaker, cheaper ranged unit with no specialized functions, is given to the crossbowman (probably for greater variety in visuals). Arquebusiers end up being a skirmisher/rifle unit unique to the Chinese and oddly outranges all muskets.
In AOE4 there are some civs with arquebus but they are only considered replacements of hand cannons. Streltsy is simply “hand cannoneer but with a unique trait” despite using the more advanced arquebus, and most other civs do not have arquebuses at all when they should.
3. Javelin
Perhaps the idea of “javelins have low damage and counter all ranged weapons” originated from AOE2 (mostly for gameplay reasons). But it remained for almost the entire series, and also Rise of Nations.
AOE3 is the exception where the javelins is either a short-ranged cavalry counter, or a generic ranged weapon with no bonus (like the in-game musket).
AOE1 has a setting where javelins are very common but it does not have them at all. The counter-archer role is given to the slinger (another unit that should not have this role).
My understanding of real javelins is a “melee weapon but ranged”, like the throwing axe. It can deal a lot of damage. It probably should be given its own role, or as an auxiliary to the melee units.
4. Sling
AOE1 slinger is an archer counter like the javelineer in later games.
AOE2 slinger is a…hand cannoneer.
AOE3 there is an infantry counter slinger and a siege slinger.
Real slings should probably be an all-purpose ranged weapon just like bows. It requires more skills so it eventually got replaced in general, but still see use in special terrains or regions with the tradition.
I guess the reason why javelins and slings are always given strange roles is because bows/crossbows are the to-go ranged weapons so they are always the standard ranged unit. Then the other ranged weapons fill in whatever role the game needs.
5. Culverin
Culverins were simply one variant of regular field artillery.
AOE3 is set in an era where most heavy equipments are variants of artillery. To differentiate their roles, the culverin which has longer range is chosen for the role of “long range, low damage artillery counter”. In reality due to its larger caliber it actually should be more powerful than falconets. The ship counter role is 100% forced for gameplay reasons.
AOE4 uses the same idea. However in the late medieval setting, I’d expect it to be simply a more advanced artillery than the “bombard cannon” (which is another weird concept directly inherited from AOE2) because there aren’t many artillery types around.
Honorable mention: Crossbow
In most games not limited to AOE, crossbows are just variants of bows or upgraded bows. This is finally fixed in AOE4.