what's the difference between a jacket, a coat and a paletot sac?
Terms used to describe clothing styles varied from era to era and from author to author. However, generally speaking:
"Coat" refers to a full-length man's outer garment. "Jacket" in the mid-19th century generally refers to a shorter garment. Obviously there is some overlap here, but a knee-length garment is pretty much universally called a "coat".
"Paletot" refers to a style of garment with no waist seam in the front, and generally no separately cut side body. This was originally an overcoat, but by the 1860's had become an accepted informal style of coat. DeVere's "Paletot Jacket" draft is an example.
I have not nailed down a definition of the term "sack coat" but "sack" or "sac" back seems to refer to a one-piece back with no seam in the middle. This is obviously looser fitting than a shaped back, which probably gave rise to the name. So "paletot sac" probably refers to a paletot with a one-piece back; which is not to say that some cutter used it to refer to something else.
Hope this helps,