A robe is more than a cloak in that it has sleeves. Notably, wizards are often in robes. In the Harry Potter books by J.K. Rowling, he wore robes for school that were black, this was Hogwarts' uniform.
Students had 3 black robes for attending classes or mealtimes, but his dress robes were bottle green and he wore these for the Yule Ball in 1994. It was part of the traditional calendar of the Triwizard Tournament, and student were ordered to wear dress robes for it.