pneumatic tire vs tyre

pneumatic tire and tyre both are nouns.

Word	Noun	Adjective	Verb	Adverb
pneumatic tire	Yes	No	No	No
tyre	Yes	No	No	No

As nouns, tyre is a hypernym of pneumatic tire; that is, tyre is a word with a broader meaning than pneumatic tire:

pneumatic tire: a tire made of reinforced rubber and filled with compressed air; used on motor vehicles and bicycles etc
tyre: hoop that covers a wheel

Other hypernyms of pneumatic tire include tire.

pneumatic tire (noun)	tyre (noun)
a tire made of reinforced rubber and filled with compressed air; used on motor vehicles and bicycles etc	hoop that covers a wheel