For all intents and purposes tags are keywords that you are recommending to your visitors to use when searching for information in your site. Because information is contained both in the posts as well as pages tags should be applied in the same way to both.
Tags are different from categories, in that they are not a way of organizing your site. Categories are structured, orderly, and static; tags are chaotic, random, and ebb and flow. Categories are broad and encompassing; tags are specific and relative. Categories (and the page tree) are meant as a way to organize the site; tags are meant to help people find relevant and cross-linked information.
Tags are a way to help users find the information they are looking for, and that information is in the pages as well as the posts.