If you received a new I-20, you have to depart the U.S. to "reactivate" your F-1 status. You may or may notneed to apply for a new visa, but can check with your home country's embassy to confirm.To remain in the U.S. between programs, you would need to request a transfer of your F-1 record.You can read more details about that here: https://internationalaffairs.uchicago.edu/transferin