What's the difference between 互相 (hùxiāng) and 相互 (xiānghù), both meaning "mutual"? I learned my early Chinese from ChinesePod, and they talked about 互相 (hùxiāng), but I just learned that 相互 (xiānghù, reversing the characters) also has a similar meaning, namely "each other" or "mutual".

(See e.g. Expressing "each other" with "huxiang", from the Chinese Grammar Wiki, which has some ChinesePod influence, talk about 互相 and not 相互.)

One example from YouDao (who sourced it from here) is:


  我们应该相互帮助
  We should help each other.


I feel like I could simply change this to


  我们应该互相帮助


without changing the meaning.  The other examples I looked at are similar (i.e., 互相 and 相互 are interchangeable), so I can't see much of a difference.  But the fact that ChinesePod seems more focused on 互相 over 相互 seems to imply something.

Question: What's the difference between 互相 and 相互?
I'd say 相互 adds a bit emphasis on the mutual effect. It may be because the reversed order draws more attention. E.g. 我们应该增进相互了解. 尊重是相互的。

互相 is more casual. e.g.我们应该互相学习. If you say 我们应该相互学习， you express a bit stronger necessity of learning from each other.