Pikes, Muskets, Swords, and Partizans
Unfortunately there isn't a realistic way to represent a "pike-push" so it's kind of like a standing up rugby scrum with armour and big sticks
The musketeers get to play with guns and black powder. And swords.
They're also usually the ones that the public want to talk to as well.
We use period drill postures and movements but once again, hand-to-hand for muskets can't be really portrayed properly.
For example, the order to close for HtoH is a variation of "Club your butts, draw your swords." Soldiers of the period would have literally used the butt-end of their musket as a club to smash peoples heads in!
We obviously don't want to kill fellow reenactors (even if they are Wascally Webels!) so it's a case of parrying an opponent and trying to jab at their body.
Officers generally ponce around in fancy clothing giving orders and hiding behind us common bods. Although one or two (both sides) like to get stuck in!
The public are always very aware of what we represent and what the actual fighting would be really like. Theres always plenty of people that want to ask questions about us, and more importantly the Civil War itself
There should be plenty of stuff on YouTube
EDIT: Sorry, missed a bit of your post!
We have living history camps at most events/battles where soldiery and officers can hang about and "live", drill in front of the public, scripted cameos etc. There are also people who are dedicated LH people and don't take part in the scrapping.