To me it's a pot if it's made out of metal, like a small single- or double-serving restaurant pot for tea or coffee that sits on your table. If it's glass, from the coffeemaker, it's a carafe, but you would still call it a pot in conversation. If it's an insulated one of the kind used in restaurants by the waitstaff, then the restaurant might call it a coffee server because they pour coffee into it from a big machine to serve, but I wouldn't call it that in some other context.
If you put an insulated pot like that, with a handle and spout for serving, in a picnic basket, you could still call it a pot of coffee, but you could also call it a flask because of the insulation. I believe it's usually thermos in AE, flask in BE, but I think flask would be understandable enough, and I don't think we would really say a thermos of coffee unless it was really the camping kind, without a handle or spout.
I personally wouldn't say a jug of coffee, I don't think, though people do sometimes say 'thermos jug' for a thermos in my part of the US.