The only civil war game I've played was Take Command: Second Manassas, a real-time game (with pause) where you play out different phases of the battle. If I remember correctly, you have a few maps available at the start, each depicting a part of the battle with a specific commander, and winning a victory unlocks the next map with that commander, which continues the battle chronologically (the battle took place over three days). The size of your command ranges from a few regiments to ten of thousands of soldiers.
Each unit has a commanding officer, and the game's schtick is that you can automate them to a degree, and then give them general orders that they carry out: attack, defend, flank left, flank right, etc. The highest commander, whose role you play (RPG!!1!), is also a unit represented on the map, and when you give an order to a subordinate, a messenger spawns from your character and gallops towards the order's recipient. This adds a realistic delay to your orders, and makes the positioning of your commander (who can be killed in battle) a strategically important decision. To top it off, messengers themselves can be killed and you then have to reissue the order.
This all sounds nice in theory, but to be honest I didn't automate anything and micromanaged the shit out of every regiment (regiments being the smallest unit you can control), so I can't really judge whether the sytem worked well. When it comes to the combat itself, it's what you would expect: regiments shoot in volleys then reload, flanking provides a big advantage, and your goal is to break enemy regiments' morale while preserving yours. Regiments have a fairly large but not unlimited amount of ammo, and you need to send them to your ammo cart(s) to ressuply. There's also artillery -- grapeshot owns -- and cavalry, which can charge in to break already weakened regiments.
I bought it on Steam back when I still used the service, and their version doesn't work unless you install the fan supermod/patch. Now there's no reason not to install that patch since it adds a lot of improvements, but just so you know, the Steam game doesn't work on its own.