I do look at a critigue partner as being MORE -- particularly more knowledgable about the craft of writing. The CP comes at the ms as a writer herself.
The Beta Reader is more of a READER. COmes at the story from a reader's perspective, not a writers. They can tell you that something's not working, or that a character annoys them, or that you left a big glaring plothole -- but they're not as good for things like POV, show vs. tell, etc.
I have both, although my dear beta reader is awesome at catching any grammar blunders that sneak past me. (My CP is not as skilled with grammar, so this works out well.) Although actually, there are grammar and spelling issues that my beta points out, and I pick the other way. <G> (Hey, grammar and spelling are sometimes right more than one way. <G>)
The Beta Reader is a term used a lot in fanfic land, and that's actually where I got my beta reader. She was the only person who called me on the carpet for a plot hole in my very first story. I immediately drafted her. <G>
Susan G.