flatiron vs smoothing iron

flatiron and smoothing iron both are nouns.

Word	Noun	Adjective	Verb	Adverb
flatiron	Yes	No	No	No
smoothing iron	Yes	No	No	No

As nouns, smoothing iron is a hypernym of flatiron; that is, smoothing iron is a word with a broader meaning than flatiron:

flatiron: an iron that was heated by placing it on a stove
smoothing iron: home appliance consisting of a flat metal base that is heated and used to smooth cloth

Other hypernyms of flatiron include iron.

flatiron (noun)	smoothing iron (noun)
an iron that was heated by placing it on a stove	home appliance consisting of a flat metal base that is heated and used to smooth cloth