laugh vs express mirth

laugh is a noun but express mirth is not a noun.

Word	Noun	Adjective	Verb	Adverb
laugh	Yes	No	Yes	No
express mirth	No	No	Yes	No

As verbs, laugh and express mirth are synonyms defined as:

Other synonyms of laugh include express joy.

laugh (noun)	express mirth (noun)
the sound of laughing
a humorous anecdote or remark intended to provoke laughter
a facial expression characteristic of a person laughing

laugh (verb)	express mirth (verb)
produce laughter	produce laughter