Help me understand garrisoning units and damage please

Sup guys.

Been playing AOE2 since 2000 on and off. Just picked it back up on steam.

I'm a little more analytical than I was 18 years ago and I'm trying to figure out the best units to garrison in castles and towers, or if it even makes a difference.

So from my observations, the units actual damage/range does not translate to the damage of the tower, right? Much unlike playing starcraft and placing units in a bunker.

I used to garrison longbownen in castles all the time when I was paying this game as a kid. Lately it seems like garrisoning villagers do the same thing.

I did some castle drops with a dozen villagers and immediately garrisoned them after building the castle to avoid damage. I was surprised it put a multiplier on the damage. All this time I thought you needed to have archers.