Chocolate pots and Coffee pots was started to be made in Chinese porcelain around 1740 probably originally after copper models sent from Europe. The first models were straight sided pots with the base wider then the top and with side handles in wood or porcelain. I am not sure that there originally were any difference in the shapes between pots for these two beverages.
Eventually specific chocolate pots was started to be made in porcelain at Meissen, Vienna and Höchst. These European chocolate pots from mid 18th century are however of straight sided cylindrical shape, have a side handle and eventually come with a swizzle stick protruding from its cover. This was to allow the chocolate tablet to be mixed and frothed up with hot milk or water.
This later shape is very rare in 18th century Chinese porcelain if it occurs at all.