I assume you're referring to a 4-button sack. The sack coat was called that because it was very much like a civilian suit coat, and it hung from the shoulders like...well, a sack. It usually had 4 or 5 buttons, including the collar, which could either be standing or turned down ("rolled") like a modern shirt. I believe it was officially referred to as a "blouse" by the Army. It was the most comfortable and practical. You'd probably be happiest with this.
The Frock coat was usually worn by unmounted troops, as it hung down quite a bit, almost mid-thigh, and was more form-fitting. Most Dress uniforms were Frocks as well, for all branches, and could be single-breasted (enlisted, and Jr. Officer) or double-breasted (Senior Officer and General).
Cavalry also wore the shell jacket, which was waist-length, fit snug, had 8 or 9 buttons, and usually had more yellow piping, and lace (cloth tape) around the collar and/or cuffs. Some were double-breasted, like frock coats. Actually, a shell jacket is pretty much a frock coat without the skirt. It looked more flashy and colorful than the sack, but really wasn't practical in the field, being so short and snug. Many had belt loops on the bottom edge so the weight of your sword/pistol would hold it down and keep it from riding up.
I couldn't resist posting what I did on your other post.