There’s also a difference depending on what kind of argument is going on. If we’re arguing about whether intelligent life exists elsewhere in the universe, well, no one really knows. No one can possibly settle that discussion by saying “I’m an astrophysicist, and I say the answer is no”. (I suppose the question could be settled by someone actually revealing themself to be an alien, but that’s neither here nor there).
If, on the other hand, we’re having a discussion about a purely factual question, the kind which could be looked up on Google, except that (for instance) we’re out in a park and have no internet access, and an accepted authority on the matter speaks up, I tend to consider the matter settled, at least for the moment.
For instance:
A: I believe there are 100,000 stars in the milky way
B: I believe there are 100,000,000 stars in the milky way
A: You’re wrong, numbnuts
B: You’re wrong, dickwad
C: I’m an astrophysicist. I happen to know that there are around (X) stars in the milky way.
Well, your cite (and several others I’ve discovered) back you up, so I owe you an apology on my strong language and my attitude of absolute certainty. However, there are many reasonable sources that back up my definition as well, including the well-known (and I think it’s fair to say - well-respected) cite in the the OP.
However…
Your cite (and each of the cites that I can find that back you) don’t even talk about what I call an “argument from authority”, namely when one says “it is so because I say it is so, and I’m an expert.” They use this term as identical to the term “appeal to authority”, and are clear that said authority is a third party. So…
Though your terms clearly have meaning outside of the what the OP intended (and what I had believed to be the only meaning), your original comment didn’t address the OP because this second meaning doesn’t relate to the OP’s clear definition.
Someone mentioned being an authority on his or her own beliefs, which is interesting because it squares nicely with the Pope question. After all, if you are such an authority that your word is law in your domain (such as the Pope), then really, any questions contingent on your authority are, at base, questions about your beliefs.
The proposition that P falls under a domain about which the Pope’s word is law.
The pope believes that P.
Therefore, P.
Since the Pope (like any person) is the authority on his own beliefs, if he asserts that he believes that P, then he cannot be said to be mistaken in saying that so. (He could be said to be lying when he says he believes that P, but that’s a whole 'nother kettle of fish.)
You have an appeal to authority when 1) does not exist. (After all, for the vast majority of domains, you can’t say that “the proposition that Q falls under a domain about which John Smith’s word is law.”)
(This post was merely an excuse to use the construction “that P.” Thank you.)