Retrofit leaves the existing frame in place and fits the new window inside it. Faster, cheaper, less disruption, and you lose an inch or two of glass. Full-frame (sometimes called brick-to-brick) takes everything back to the rough opening.
Full-frame is the right call when the existing frame is rotten, when there is no insulation or flashing behind it, or when you want the glass area back. It is also the only way to know what is actually in the wall. If a quote does not say which one it is, that is the first question to ask.