I'm hunting through the docs but can't find an answer to this.

What are the differences between the three types of body mentioned?

Thanks

Tom

From the Box2D manual:

b2_staticBody
A static body has does not move under simulation and behaves as if it has infinite mass. Internally, Box2D stores zero for the mass and the inverse mass. Static bodies can be moved manually by the user. A static body has zero velocity. Static bodies do not collide with other static or kinematic bodies.

b2_kinematicBody
A kinematic body moves under simulation according to its velocity. Kinematic bodies do not respond to forces. They can be moved manually by the user, but normally a kinematic body is moved by setting its velocity. A kinematic body behaves as if it has infinite mass, however, Box2D stores zero for the mass and the inverse mass. Kinematic bodies do not collide with other static or kinematic bodies.

b2_dynamicBody
A dynamic body is fully simulated. They can be moved manually by the user, but normally they move according to forces. A dynamic body can collide with all body types. A dynamic body always has finite, non-zero mass. If you try to set the mass of a dynamic body to zero, it will automatically acquire a mass of one kilogram.

http://www.box2d.org/manual.html - Chapter 7