stupid person vs pudding head

stupid person and pudding head both are nouns.

Word	Noun	Adjective	Verb	Adverb
stupid person	Yes	No	No	No
pudding head	Yes	No	No	No

As nouns, stupid person and pudding head are synonyms defined as:

Other synonyms of stupid person include dolt, dullard, pillock, poor fish, pudden-head, stupe, stupid.

stupid person (noun)	pudding head (noun)
a person who is not very bright	a person who is not very bright