The most common design of the bubby pot (a.k.a. "suckling pot") is pictured at left. It's shape was designed by Dr. Hugh Smith around 1770 as an improvement over the other widely used designs available - including the ceramic nursing bottle. The name "bubby" was derived from an old world euphemism for female breast and its unique design attributes included having a lid (with a small air hole used to regulate content flow) and a closed and perforated spout end (to better duplicate natural feeding mechanics).

Dr. Smith's first prototype was most likely made of pewter or silver (see photo below) with its ceramic variations following thereafter.

Now the bad news, the pot's design (with its impossible to clean spout and perforated spout end) contributed significantly to infant mortality. 

One comes across ceramic pots and/or spouted cups similar to those at left and lower left when collecting.

To me the distinction between them is whether or not they have a perforated spout end.  If they do I consider them to be suckling pots (similar to bubby pots) and if they don't I consider them to be feeding cups. 

Similar designed suckling pots also came in silver and pewter (see example below).

This is a wonderful example of a transfer-printed suckling pot with its contents regulated not with a lid (like a bubby pot) and small air hole but with a larger thumb sized hole similar to nursing bottles.

Variations of these types of designed pot were also made in silver and pewter (see example below) except their spout ends were a single hole as opposed to perforated. 

What to call this example is a throw of the dice. While it is shaped and designed like a typical feeding cup it also has a suckling pot spout (i.e., perforated end). Safe to say the one pictured at left was hardly if ever used evidenced by its perfect unrepaired spout tip.