Models and Methodologies
To a first approximation, the terms are used to characterize both research methodologies on the one hand, and models (or features of models) on the other. I shall be primarily concerned with the issues surrounding top-down versus bottom-up methodologies, but we risk confusion with the other meaning if we don't pause first to illustrate it, and thereby isolate it as a topic for another occasion. Let's briefly consider, then, the top-down versus bottom-up polarity in models of a particular cognitive capacity, language comprehension.
When a person perceives (and comprehends) speech, processes occur in the brain which must be partly determined bottom-up, by the input and partly determined top-down, by effects from on high, such as interpretive dispositions in the perceiver due to the perceiver's particular knowledge and interests. (Much the same contrast, which of course is redolent of Kantian themes, is made by the terms "data-driven" and "expectation-driven").
There is no controversy, so far as I know, about the need for this dual source of determination, but only about their relative importance, and when, where, and how the top-down influences are achieved. For instance, speech perception cannot be entirely data-driven because not only are the brains of those who know no Chinese not driven by Chinese speech in the same ways as the brains of those who are native Chinese speakers, but also, those who know Chinese but are ignorant of, or bored by, chess-talk, have brains that will not respond to Chinese chess-talk in the way the brains of Chinese-speaking chess-mavens are. This is true even at the level of perception: what you hear--and not just whether you notice ambiguities, are and susceptible to garden-path parsings, for instance--is in some measure a function of what sorts of expectations you are equipped to have. Two anecdotes will make the issue vivid.
(The whole paper is now available in Daniel Dennett, Brainchildren, Essays on Designing Minds, MIT Press and Penguin, 1998.)