E-Publisher or Vanity Press?

Silly question, I know, but I'm curious, are all e-publishers Vanity Presses?

A lot of agents say not to mention your publishing credits if your manuscript was published by a vanity press. But how do you know for sure whether a publisher is a vanity press? It can't be as simple as having "Press" in the name can it?

EX:

Aspen Mountain Press
Carina Press
Eternal Press
Lillibridge Press
Lyrical Press

So my question is this? Are the above publishers vanity presses? And if it's not posted on their website for everyone to see, how does one tell whether a publisher is a vanity press?

This has been eating at me for days, so any help you all can give me is appreciated!!

Thanks Veinglory!! Why is a vanity press so bad?

Ah, excellent. Thanks for the information!!