oil rig vs offshore rig

oil rig and offshore rig both are nouns.

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

As nouns, offshore rig is a hyponym of oil rig; that is, offshore rig is a word with a more specific, narrower meaning than oil rig:

oil rig: rig used in drilling for oil or gas
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

Other hyponyms of oil rig include drilling platform.

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