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.
There are crowd cheers which get the spectators involved by yelling letters, colors or other words on cue. There are also show cheers which are simply words that explain something about the team. Here is one of example of a crowd here and one example of a show cheer. Hey we're back. Better than before.