I might put that simply as:
Gate: a structure that you "rent" from the airports you serve (including your main base and focus cities). The price for a gate depends on how many passengers actually use the airport (between 50,000 for the small regional airfields and 350,000 for the mega-hubs), and the more gates you get (at least 4), you can form a "focus city" connecting more routes.
Terminal: a group of at least five (5) gates that you build your own that could be separate from the main "terminal" (all rented). The price of building a terminal is dependent on the airport's current passenger loads and how many gates you're willing to build to form one. Usually, you build a terminal when you're sure that your airline is working very well from either your main base or focus cities, so check your bank balance and gates before building one; it can be an expensive move, but I can tell you that it's worth it!
