counterfactual vs contrary to fact

counterfactual and contrary to fact both are adjectives.

Word	Noun	Adjective	Verb	Adverb
counterfactual	No	Yes	No	No
contrary to fact	No	Yes	No	No

As adjectives, counterfactual and contrary to fact are synonyms defined as:

counterfactual and contrary to fact: going counter to the facts (usually as a hypothesis)

counterfactual (adjective)	contrary to fact (adjective)
going counter to the facts (usually as a hypothesis)	going counter to the facts (usually as a hypothesis)