Ancestry's classifications of the closeness of the matches are based on probabilities, so yes, a cousin classified as a probable fifth cousin could be a fourth or sixth or seventh. You may have received smaller or larger matching segments than average just by chance. Another factor, I think, is multiple relationships. You may get a match if you are ninth or tenth cousins with a person three different ways. I may be wrong about this, but it seems true from my own experience. :) There is a post somewhere on these boards about why Ancestry's autosomal test may be more reliable than other autosomal tests with regard to the distant matches. If I can find it, I'll post a link.
Re: "Do the other types of DNA yield actual matches?" I am not sure that I know what you mean by this.