doormat vs welcome mat

doormat and welcome mat both are nouns.

Word	Noun	Adjective	Verb	Adverb
doormat	Yes	No	No	No
welcome mat	Yes	No	No	No

As nouns, doormat and welcome mat are synonyms defined as:

doormat and welcome mat: a mat placed outside an exterior door for wiping the shoes before entering

doormat (noun)	welcome mat (noun)
a mat placed outside an exterior door for wiping the shoes before entering	a mat placed outside an exterior door for wiping the shoes before entering
a person who is physically weak and ineffectual