In your dress you are demonstrating self-respect, your respect for the company and the interview opportunity, and your ability to dress appropriately in social and business situations. You are demonstrating that you are ready for and want work in a professional environment. It does not matter if the interviewer is in business casual. You should be in business professional. Sometimes companies invite students for a second interview or a mixer and specify business casual.
Standards vary a great deal from company to company.
Companies typically do not hire students who do not know how to dress appropriately.