Is there any difference between 相濡以沫 and 以沫相濡? I encountered the following sentence:


  他们都一直相濡以沫，患难与共。


I looked up the entry on Pleco, and although it shows the meaning, it also redirects toward 以沫相濡, which seems to have the same meaning (as well as 濡沫).

So I wonder whether it is OK to assume that these are just synonyms and have no difference, or have any meaningful (even if tiny) difference.

Also, is this kind of Chengyu (the first and last two characters are flipped) common? And if it is practically same, why do these different forms exist in the first place?
Also, is this kind of Chengyu (the first and last two characters are flipped) common? 


No, it's not common. 

相濡以沫 is the most people would use. 以沫相濡 is not that common, though we can understand it. 

We don't usually flip the character order in idioms.