Yes! As long as the building is relatively stable, these sorts of moving companies are able to move all sorts of buildings from one place to another. Sheds and trailers are the most common, but there are also cases where they have moved barns, business buildings, and all other sorts of buildings to a new location or one reason or another.
Not all house moving companies will move other buildings though. If you’re considering a move of another building, ask ahead of time and see if you can find a connection that makes sense for you.