Cheer someone on: you root for them/ show support Ex: Go Bobby! Make it to the finish line! You can do it! - someone is cheering Bobby on Cheer someone up: Make someone feel better (because they are sad). Ex: I tried to cheer Bobby up because his girlfriend dumped him. The students cheered the teacher up with an apple.

These do not mean the same thing. The two "cheers" differ - cheering can mean literally shouting at someone, and can also mean making someone feel better by giving them "cheer" (good feelings). Cheering someone up means you are making them feel happy, usually by showing them support. (Think of it as "lifting up" someone's feelings). Cheering someone on usually refers to sports or when you are encouraging someone (usually from the sidelines) to do a great job at whatever they are doing. (Think of this as cheering someone to "continue on" with what they are doing in an encouraging manner). Hopefully this helps :)