Is there a difference between brown and white champignons?
Check this site: What’s the difference between cremini and white mushrooms?  

Brown(Baby Bella or Cremini) mushrooms have earthier flavor than the whites, you could use them based on your dishes' style or presentation.  

And the storing should be the same. Put them in some brown bag with normal temperature and do not freeze them. Slightly wipe the dust or dirt just before cooking, no need to wash by water.