They are similar. They are not interchangeable.
"Really?" is the more common and more standard expression. It expresses mild surprise. It is regular, standard English.
"For real?" is stronger. It expresses total disbelief, not just doubt or surprise. It is scornful. It is informal and colloquial. It is not quite standard English. It became popular around 1950, according to a slang dictionary.
"I'd like to eat at McDonald's."
"Really? We usually go to Red's Sub Shop."
"No, I just feel like McDonald's today."
"OK, sure."
"I'd like to eat at McDonald's."
"For real? You've got to be kidding. How can you even think of eating at that awful place?"