Your classmate is someone who goes to school with you. It's hard to believe when you first start college that some of your classmates will become your very best friends.
Your school friends are your classmates, and so are the fellow students you barely know at all. In a small class, you get to know most of your classmates fairly well, while in a large lecture even your teacher might not know all your classmates' names. The word dates from the 18th century, a combination of class, from the Latin classis, "class or division," and mate, "fellow or comrade."