For lenses of fixed focal length (often called prime lenses) the usual focusing method is to move the whole lens. There are exceptions, particularly with high-end and low-end lenses. For cheap lenses only one element, often the front element, may move. For some high-end lenses, and almost all zoom lenses, the focusing may be achieved by moving internal elements.
There are some high-end lenses that combine both effects - ie they move the whole lens, and they move internal elements (floating elements). In those cases the internal element is usually moved to improve the image quality, not to focus. Nikon CRC (Close Range Correction) lenses are like that. There are some lenses, like the old Zeiss 40 mm FLE Distagon (FLE = Floating Lens Element), where the internal movement and focusing mechanism are separate - the user has to set the floating element, then focus.
Macro lenses are similar in that they may be focused by moving the whole lens without moving any internal elements, or they may focus by moving internal elements, or they may have a combination of the two. As well as improving the optical design for different distances, the floating elements may also reduce the focal length as the lens is focused closer. This is common among recent Nikon macro (Nikon call them 'Micro') lenses. This enables the lens to focus very closely without too much lens extension - the mechanism that moves the lens further from the image plane need not have such a large travel as it would have to have if the focal length stayed the same.
The performance of macro lenses at 'normal' distances varies a lot from design to design. The new 60 mm AF-S Micro-Nikkor is outstanding in this respect - it is good at all distances.
Best,
Helen