Counterfactuals

Discuss the wiki-tag on this page. Here is the place to ask questions and propose changes.
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I always thought that counter-factual means some message that is not conforming to reality. Was my personal understanding of semantics of this word wrong? Or maybe, your definition and my intuitive understanding can be reconciled? Isn't counter-factual as contrary to past decisions a special case of counter-factual as not conforming to reality? If yes, can the word be used in both senses, dependently on a context?