Yes, it's limited to size.
What I think you mean is to have curated content or special pages based on certain specifications (geo, age, language, whatever), but adaptive design is related to size and/or device (for example gestures, touch enabled behaviors and such), which in turn affects size since different devices will have different screens.
Nevertheless, you have 2 basic options:
Here you have only one page that "reacts" to screen sizes by using media queries. By using different techniques you can also change content, but in its coding is always the same page
Here you have a set of pages (that may or may not be responsive as well) or stylesheets that are served based on device. Usually uses 3 sizes: desktop, mobile, tablet. Here you can change content display at will, and many times is used to mock a mobile app design. Due to this, many people thinks adaptive design is the same as a mobile app, which is NOT THE CASE. Adaptive design may also be used to provide capabilities one device may have but the other may not, like multi-touch gestures in mobile/tablet or giant sized images in desktop
Now, if you talk about serving different content based on certain specifications like location, age, language, custom preferences, cookie tracking and so on, there are many different techniques and approaches and the answer would exceed the limits of your question. But yes, you can do that, although it's not adaptive design