pudding face vs mug

pudding face and mug both are nouns.

Word	Noun	Adjective	Verb	Adverb
pudding face	Yes	No	No	No
mug	Yes	No	Yes	No

As nouns, mug is a hypernym of pudding face; that is, mug is a word with a broader meaning than pudding face:

pudding face: a large fat human face
mug: the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)

Other hypernyms of pudding face include countenance, kisser, phiz, physiognomy, smiler, visage.

pudding face (noun)	mug (noun)
a large fat human face	with handle and usually cylindrical
	the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)
	a person who is gullible and easy to take advantage of
	the quantity that can be held in a mug

pudding face (verb)	mug (verb)
	To stare awkwardly
	rob at gunpoint or with the threat of violence