hawker vs muffin man

hawker and muffin man both are nouns.

Word	Noun	Adjective	Verb	Adverb
hawker	Yes	No	No	No
muffin man	Yes	No	No	No

As nouns, muffin man is a hyponym of hawker; that is, muffin man is a word with a more specific, narrower meaning than hawker:

hawker: someone who travels about selling his wares (as on the streets or at carnivals)
muffin man: formerly an itinerant peddler of muffins

Other hyponyms of hawker include chapman, cheapjack, crier, sandboy, transmigrante.

hawker (noun)	muffin man (noun)
someone who travels about selling his wares (as on the streets or at carnivals)	formerly an itinerant peddler of muffins
a person who breeds and trains hawks and who follows the sport of falconry