We want to show you examples of cups that are frequently confused with pot de creme cups. There simply is not a lot of history available about porcelain objects to always determine their specific role as part of the dining room place setting. Given that, sometimes it simply not clear what the function of the object may be.
The cup shown on the left is a tea cup with a lid. The lid helps to keep the tea warm. These cups are typically larger than a pot de creme cup, holding at least 6 ounces rather than 3 ounces which is the average pot de creme capacity.
Made by Apilco. Given their straight sides, no handles and overall utilitarian appearance these little pots are probably used to store confit, pate, or cheese. Apilco currently makes a pot they sell as a pot de creme which has small "lions head" handles, similar in shape to the marmite cups shown above. The little tureen is more intended for soups.
We are not experts at Asian pieces but our best guess here is that these are either sake or tea cups, but most likely tea cups given the size and the cover. The cups measure 3 1/2" high x 2" wide.