These are both great responses to the question. From my understanding, the difference between ideology and inquiry is similar to, but not exhaustively explained by, the difference between orthodox religion and empirical science. While the traditional Christian worldview, for example, sees human existence as governed by a benevolent deity who is the cause of all creation, and thus would not need further explanations for, say, why the universe exists, or what stars are made out of, the empirical scientist seeks answers for these very questions in order to discover new facts about the observable universe, extrapolating from their observations what positivists might call "true knowledge" or "natural laws." In the same way, ideology - whether it's religious, legal, political, economic, cultural, etc. - represents to a person the world through a very specific "interpretive framework," that is, a self-contained way of conceiving one's relationship to their conditions of existence; while with inquiry, one comes to understand things through what the Oxford Dictionary describes as a "process to find out the cause of... or to find out information about something." In short, ideology attempts to make sense of our conditions of existence within a system of thought or belief, while inquiry is a process of "finding out the facts" and determining what is true through observation, methodology, and data collection.
