Why is the intermediate Shabbos of a festival referred to as Shabbos Chol haMoed (and not something else, e.g. Shabbos haMoed)? Aren't Shabbos and Chol opposites?
The intermediary days of Succot and Pesach are known as "Chol Hamo'ed". It is a "mixed term", as a "mo'ed" implies a holiday with work restrictions, as many think of it. the "Chol" part means "profane" or colloquially, "weekday". During these days, work that would result in a monetary loss (that's a loose definition. See O.C. or your rav for details on what work is permitted.) is permitted during these days.
You are correct that Shabbat and "Chol" are opposites. But, the term "Shabbat" is a modifier for the entire term "Chol Hamo'ed" which describes the entire 4 or 5 days, themselves. In other words think of it as the Shabbat of the "Chol Hamo'ed" period.