Fixed routers are just that: fixed. They are used mostly for edge work on doors, cabinets, tables or any other flat surface. With a fixed router, the tool remains in the same position on a router table as the material is moved against the router bit. The router is set and locked to the desired depth of the cut. This is especially handy if you have more than one piece that requires the same type of cut.
Plunge routers come in varying horsepower designations that determine the tool's weight and capability. These types of routers are hand-held and are best for work inside the edges. By "plunging" the router into the wood, you can create in-cut designs or grooves. This type of router takes some practice and patience to maintain a consistent depth. It accepts a wide range of bits for different types of edges, from rounded to straight to angled.
The palm router is a small, lightweight plunge router used mostly for decorative inlay work and creating dovetails, cutouts, slots and hinge mortises. By virtue of its name, the router is controlled by guiding it with the palm of your hand. Many palm routers offer variable speed options and an adjustable bit size holder. You can also attach a fixed base to a palm router to ensure repeat cuts are consistent in depth or when using it for edge work.
Heavy-duty use routers that are not fixed are also known as bodygrip routers. They have more horsepower than palm routers and a bigger base, which allows for heavier cuts. Unlike the palm router, the bodygrip is guided with handles located on the left and right of the base and can be used for edge finishing, boring or inlay cuts. These routers usually include special features that allow you to switch quickly from table guide to free-hand application.