If you have an F-1 visa and you want to do an internship, you should apply for a CPT at your school’s international student office. You only qualify for a CPT after you’ve completed one full year of studies.
J-1 visa holders who are students at an American school are eligible for Academic Training (AT) during or after completing their studies. AT includes internships.
J-1 visas are also available for young peope who have recently graduated from a university in their home country and would like to pursue an internship in the US.
These are called J-1 intern or trainee visas, for more info click here.