Disclaimer: The information in this post is what I have gleened from sources, but the lines seem very blurry between these styles, and so if I am wrong about something, please leave me a comment and correct me!
A caraco is a long-length jacket with a fitted back, like a robe a l'Anglaise. The length of the skirt of these jackets seems to be about mid-thigh, and the skirts usually have inverted box pleats at the back, often pressed but sometimes left loose. Caracos typically have 3/4 length sleeves with flounces. Examples of caracos close severals ways, with lacings over a stomacher, pinned to a stomacher, with "flaps" that hook across a stomacher, or with a comperes front (a false front made to look like a stomacher, that closes at the center with hooks or buttons), or edge-to-edge by hooks.
|The matching caraco and petticoat from the V&A|
|A interesting caraco with an extremely low-cut front|
A Pet en l'ier
A pet en l'ier jacket is a garment of mid-thigh to mid-hip length, with a saque back, that is, watteau pleats at the back. This jacket usually has 3/4 sleeves with flounces, and closes over a stomacher or with a comperes front.
|A short-length pet-en-l'ier from KCI|
A pierrot is a a very short jacket, actually more of a bodice with a ruffle or flounce added onto the back. Pierrot jackets came into style later in the century, and often closed edge-to-edge with hooks or interior lacings. They were most commonly long-sleeved, and worn with walking-length skirts, puffy fichus, and monster-sized hats.
|A zone-front pierrot|
|A pierrot from KCI - notice the lack of jacket skirt in front|
A casaquin jacket is that of short length, about mid-hip, but still with a flared skirt and pleats at the back. It has a fitted back, like a robe a l'anglaise, and may or may not have seams at the waist. Casaquins may have 3/4 length of full-length sleeves, and close over a stomacher. The hallmark of a casaquin appears to be the lacey trimmings.
|The casaquin featured in this week's Costume Analytics|
So there you have it. I did not cover the Polonaise, the Riding Habit, Redingote, or the Figaro, but hopefully this little primer has been helpful to you all!