两个都是副词，都表示事实上、实际上。但查一下英文释义可能会更清楚一些。

In reality: used to imply that one would expect the fact to be the opposite of that stated; surprisingly. 这个常用来纠正前面所述的相反的事实。例如： This problem should not occur, but in reality it dose. 而In fact: in reality or actuality. 更偏向于现状，适合陈述事实，例如：In fact, this problem should not occur.