1、意思上的區別
keep up with：緊跟跟上，不落人之後齊肩並進。
catch up with：趕上追上和…算舊賬使…最終嚐到苦果。
2、用法上的區別
keep up with ：是有關於你學業／工作的水平而言。（褒義）
catch up with：是有類似於追上的意思。（中性）（或者有自貶意思）
例句：
①、keep up with
She was skipping to keep up with him.
她連蹦帶跳地走着，好跟上他的步伐。
She began to walk faster， but he lengthened his stride to keep up with her
她開始加快步子，但他加大了步幅跟着她。
②、catch up with
I couldn't catch up with him.
我攆不上他。
There's still time to catch up with them.
還有時間追上他們。
We'll do our best to catch up with the advanced world levels.
