For an argument to have any epistemological or dialectical force, it must start from premisses already known or believed by its audience, and proceed to a conclusion not known or believed. This, of course, rules out the worst cases of Begging the Question, when the conclusion is the very same proposition as the premiss, since one cannot both believe and not believe the same thing. A viciously circular argument is one with a conclusion based ultimately upon that conclusion itself, and such arguments can never advance our knowledge.
All circular logic is not Begging the Question, but used fallaciously the terms are effectively synonymous. If a premise is not truly needed to establish a proposition, then its circular nature reinforces rather than fools. Use with care, if only because an unscrupulous opponent may charge circularity.
Circular logic is not always fallacious. For instance, we know that 2 + 2 = 4 in part because 4 - 2 = 2.
The best use of circular logic, however, is indirect: if in reasoning back to our premises we encounter a contradiction, reductio ad absurdum alerts us to an error somewhere, either in our reasoning or premises. Care must be exercised here as well, because we may not find an error but still have a false conclusion. Something external to the loop must validate it, and nothing must invalidate it.