offshore rig vs oilrig

offshore rig and oilrig both are nouns.

Word	Noun	Adjective	Verb	Adverb
offshore rig	Yes	No	No	No
oilrig	Yes	No	No	No

As nouns, oilrig is a hypernym of offshore rig; that is, oilrig is a word with a broader meaning than offshore rig:

offshore rig: drilling rig consisting of an offshore platform (floating or fixed to the sea bed) from which many oil wells can be bored radially
oilrig: rig used in drilling for oil or gas

Other hypernyms of offshore rig include drill rig, drilling rig, oil rig.

offshore rig (noun)	oilrig (noun)
drilling rig consisting of an offshore platform (floating or fixed to the sea bed) from which many oil wells can be bored radially	rig used in drilling for oil or gas