Generally, each project has its own folder (usually within the solution's folder), although it is possible to place them both in the same folder. It is also an option to show all files, including those that are not part of a project. If you have the option enabled to display all files then an item should should appear grayed out in any projects which it is not a part but whose folder it is present in.
If the projects are in different folders and you add an item from the first project to the second, you can either add it normally, which will place a copy of the file in the second project's folder, or you can add it as a link, where it is a shortcut pointing to the original file (it will be displayed with the Windows shortcut icon).
Most likely, you have the two projects in different folders and are adding the item from one project to another normally (i.e. not a link) which means that the file will be copied. If you exclude it, it will still be present in the second project's folder, hence it is displayed grayed out. If you delete it, it should not delete the original.