At the moment, the frontend is somewhere between global and context. It is not context-specific and can't be limited thus, but at the same time, it doesn't search everything (e.g. comments).
WP should have 2 search box widgets:
More on the lines of the current search, with additional scope, e.g. to include comments, custom posts, etc.
Search in all pages, or all posts, or a particular CPT (e.g. forums, events, places, etc), or within a category, etc.