For certain and For a fact

For certain adverb - Definitely or positively (`sure' is sometimes used informally for `surely').

For a fact and for certain are semantically related in definitely topic. In some cases you can use "For a fact" instead an adverb phrase "For certain", when it comes to topics like accurately.

For certain and for a fact are semantically related in definitely topic. You can use "For certain" instead an adverb phrase "For a fact", if it concerns topics such as accurately.