It's actually all related, most likely (be sure and read the last update to the relevant dreamhoststaus.com post):
We are continuing to move data off of the problematic file server but it’s a bit of a catch-22 because customers on that machine are continuing to add data at a very high rate. It filled up this morning for a while causing device full errors as well as mail problems and issues serving websites (when these fill up it causes problems across the board). ... "
You may be able to fix that yourself, following these instructions: