Real is an adjective meaning “genuine” or “authentic,” or having a “verifiable existence.”
Really is an adverb used to add emphasis and means “in fact,” “genuinely,” or “indeed.”
Careful writers do not use real as an adverb:
He ran real fast.
He ran really fast.
Example: He was sure that what he saw was real. Later, he had a hard time persuading anybody that he had really seen it.