1、意思上的区别
keep up with：紧跟；跟上，不落人之后；齐肩并进。
catch up with：赶上；追上；和…算旧账；使…最终尝到苦果。
2、用法上的区别
keep up with ：是有关于你学业／工作的水平而言。（褒义）
catch up with：是有类似于追上的意思。（中性）（或者有自贬意思）
例句：
①、keep up with
She was skipping to keep up with him.
她连蹦带跳地走着，好跟上他的步伐。
She began to walk faster, but he lengthened his stride to keep up with her
她开始加快步子，但他加大了步幅跟着她。
②、catch up with
I couldn't catch up with him.
我撵不上他。
There's still time to catch up with them.
还有时间追上他们。
We'll do our best to catch up with the advanced world levels.
我们将努力赶上世界先进水平。
