There is only one slight difference between paper pulp and paper casting, and that is mainly a matter of opinion. You can cast any type of paper pulp that will hold the impression, but some people feel that Paper Casting (note caps) should only be made from pulp that has never been formed into paper. Personally, I consider that something of an elitist opinion.

It is true that you can use an adhesive (cellulose adhesives may be the better type), but you can do it with nothing but pulp and water. 

Actually, much of the commercial papier mache made during its height of popularity in England used no adhesive.

"A lot of the websites I went to stated that I could use the paper casting method to create paper relief instead of putting it into a mold."

I'm not sure if this is what you meant to say. Paper casting is pulp that is pressed into a mold. If you wanted to drain more water out of it to the point you had a clay-like material that you could form by hand, that would be pulp papier mache.

Paper casting usually requires a mold of some sort, as far as I've ever known.  The pulp is often drained on a porous surface, then applied to the mold while still quite wet, and the excess moisture removed by gently patting with clean, dry rags. When almost dry, the mold is removed.

The type of pulp you would require for casting would have to be fairly fine and soft to get an accurate cast from the mold. Cotton paper fibers would be ideal. I've never heard of anyone advising use of magazine-type or other treated paper for casting. Cardboard or sticker paper, never. Soft and fibrous are the qualities you need.

Without adhesive, you shouldn't need a mold release.  With adhesive, you probably wood, depending upon the mold surface.

Whenever you want to try something new like this, it would be best to make up a small batch and experiment with it, rather than going directly into a big project and find a major flaw. I once did a paper casting into a metal form, using cotton paper fiber mixed with methyl cellulose. Busy with other things, I forgot about it until it was completely dry. Dry and STUCK. I couldn't even pry it out without damaging the mold. So I just had to fill the mold with water and let it soak enough so I could re-process the fiber. At least I could do that with the methyl cellulose adhesive. I would have been in trouble with a more permanent adhesive.
Start small.

There quite a nice book on basic paper casting that is in many libraries:  The Complete Guide to Paper Casting by Arnold Grummer.

Sue

Random question:  Would fabric scraps in small amounts help any with paper projects?  Such as casting, pulp (pulp especially), etc?  >.> I have a lot of tiny fabric scraps that I'd liek to find a use for and just wondering ^^