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