If you are using Foundation framer, symbols and components can only be used in the projects in which they are created. In RSD2 components can be saved in a component library to be used for other projects too.
Since you ask your question in the FF thread, I assume you are using that programme, and here is what I would do: Save a project with the desired component(s) as a new theme. If you have symbols, then make components out of them. Then start your next project, where you want to reuse the components, with that theme you made.
As far as I know CC will enable component sharing between projects, even between users, in some future update, but whether that will be for RSD only, or for the two other programmes too, remains to see.