The difference between Actually and In reality
Actually is also adverb with the meaning: in act or in fact.
In reality is also phrase with the meaning: when actually done or put into practice.
check bellow for the other definitions of Actually and In reality
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Actually as an adverb (modal):
In act or in fact; really; in truth; positively.
Examples:
"Actually, I had nothing to do with that incident."
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Actually as an adverb (obsolete):
Actively.
Examples:
"Neither actually ... nor passively.'' — Fuller."