in the fact与in fact的区别在于在句子里面的作用不同。
1. in the fact，后面通常接that引导的同位语从句；
或者in和前面的动词构成固定词组，the fact是这个词组的宾语。
例如：
He persevered in the fact. （persevered in坚持是一个词组）
他力言坚持这事实。
It lies, instead, in the fact that the deal got done at all.
还有一个事实就是这笔交易已经彻底的完成了。
To some degree， there is some truth in the fact that our mind creates reality.
某种程度上我们的思想确实能创造现实。
2. in fact：事实上，实际上。介词短语，固定词组，在句子里面常常作状语。
例如：
I didn't fail the exam; in fact I did rather well!
我没有考不及格，事实上，我考得不错！
That sounds rather simple, but in fact it's very difficult.
那听起来很简单，但实际上非常难。
In fact he could scarcely have spent his time more profitably.
事实上他几乎不可能把他的时间花得更有益了。