Kinematics
Kinematics is the way in which individual parts of the robot with respect to each other. Kinematics is only concerned with position and speed (the first derivative of position).
Dynamics
Similar to kinematics, but cares about acceleration and jerk too. Where Kinematics is only concerned with position and speed (the first derivative of position), Dynamics are also concerned with the second and third derivative of position (Acceleration and jerk).
Locomotion
The way a robot moves through its environment.
Locomotion includes very different concepts of motion, including rolling, walking, running, jumping, sliding (undulatory locomotion), crawling, climbing, swimming, and flying. The mechanisms that might achieve these feats could be drastically different in terms of energy consumption, kinematics, stability, and other capabilities required by the robot that implements them.
Manipulation
The way a robot moves objects in its environment.
Most mechanisms capable of Locomotion can also be used for manipulation with only minor modifications. Most industrial manipulators consist of a chain of rotary (or revolute) actuators that are connected by rigid links. In general, they are equipped with six or more independently rotating axes—we will see why further down below. In addition, modern industrial manipulators have the ability to not only control the position of each of its joints, but to also control the torque at each individual joint; this capability allows control over the compliance of a robot, which in a mechanical sense is the inverse of stiffness.