I do not understand what the difference between a cheer and chant is. There is a simple rule of thumb that you can use to determine what is a cheer or a chant.
Chants are normally short and repeated several times.
They often have a distinct beat that is easy to follow for the crowd. Here are some examples of chants. Defense hold tight, Fight Pirates fight. Green lets go Defense take that ball away. Cheers are often longer, and only used one time.