The difference between Certainly and In fact

Certainly is also adverb with the meaning: in a way which is certain.

In fact is also phrase with the meaning: resulting from the actions of parties.

check bellow for the other definitions of Certainly and In fact

Certainly as an adverb:

In a way which is certain; with certainty.
Certainly as an adverb:

Without doubt, surely.

Examples:

"The accident was certainly caused by human error."

"That was certainly sweet of him."

"You may certainly join us for dinner."
Certainly as an adverb:

An emphatic affirmative answer; of course.

Examples:

"Would you like it with ice?&emsp; Certainly, and with lemon please."