Solid graphite pencils, sometimes known as woodless pencils, are, as the names would imply, without wood, just solid graphite. Well, mixed with some clay. But they're pencils which are all core. They usually have a thin coating so they don't mess up your hands, but they can be used at a low angle to fill wide areas, which makes them perfect for some styles of art.
They also feel a bit heavier, which can give them a pleasing heft.