contrary to fact vs counterfactual

contrary to fact and counterfactual both are adjectives.

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

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

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

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