I've seen the terms "referee" and "reviewer" both used to describe a person who gives feedback to a paper in a journal submission. Are there differences between the two terms? Is one used in some situations where the other isn't?
My experience is that usage varies. In my field, it is common to use 'referee' for the person who anonymously comments on a paper submitted to a journal, and 'reviewer' for the person who writes about a paper already published to appear publicly in a database. However, people I know in similar areas use 'reviewer' for the first meaning. To confuse things more, there are some discussions underway about changing the publishing model, which would have the effect of essentially combining these two situations.
Typically they are synonymous (see this wiki entry). Some journals use one term or another, and some use both. Some fields may tend to use one more than another, but I don't know. However, my impression is that the term "referee" means someone who makes a thorough evaluation of a paper (one should check correctness and make detailed suggestions if appropriate), and the term "reviewer" is more general for someone whose opinion is solicited.
In math, full refereeing takes a considerable amount of effort and many journals now solicit quick opinions from experts to determine if a paper should go through the full refereeing process. The experts who give brief opinions could be considered a kind of reviewer (in practice, I haven't heard this term applied here, but calling them something like "preliminary reviewers" seems reasonable), whereas they should not be considered referees.
They are not synonymous. A referee decides whether a contribution is to be accept or not for publication. A reviewer provides information on published articles and books. A review of a academic work gives a brief and clear account of its contents. Reading the review is not intended to be a substitute for reading the original work; the primary purpose is to help the user to decide whether he or she needs to read the original. Therefore, the main results of the paper should be briefly described, preferably in a non-technical manner.
I think in practical terms both do the same thing. In theory a reviewer just reviews while a referee also decides whether to accept or not.
In more practical terms, when a referee delegates the reviewing process to one of their post-grads, the post-grad is a reviewer but not a referee (and yes I know this "never happens").