Simone两者区别就是：cheer up可以做及物动词和不及物动词，而cheer on只做及物动词。
具体如下：
1、cheer up
做及物动词时，意思是“使...高兴/振奋塌嫌做起来”，宾语一般是sb/oneself
如：You should cheer him/yourself up.
做不及物动词时，意思是“（自己）高兴/振奋起来”，此时无宾语，不用被动语态
如：Hearing the good news, I cheered up.
2、 cheer on只做及者氏物动词，意思是“向...欢呼；为...鼓劲加油”，可以加sb/sth做宾语（但sth比较少用）。
且on是副词，如果宾语是名词，则宾语放在cheer和on中间或放在on后都可以。如果宾语是代词，则宾语只能放在cheer和on的中间。
如：Why not cheer on his wonderful performance?
cheer up
1、I think he misses her terribly. You might cheer him up
我估计他是太想念她了。也许你可以让他打起点儿精神来。
2、I wrote that song just to cheer myself up
我写那首歌是给我自己打气的。
3、Cheer up, better times may be ahead.
打起精神来，好日子也许还在后头呢。
cheer on
1、A thousand supporters packed into the stadium to cheer them on
1,000名支持者挤进体育馆里为他们加油。
2、Most will probably be cheering on their favourite players.
多数人大概都会为自己喜欢的球员加油。
3、You get to show your support and cheer on to victory.
你团衡能显示您的支持和对胜利的欢呼。
