Average speed is defined as the total distance traveled divided by the total time, while average velocity is the change in position divided by the time interval for that change. In straight-line motion, average speed equals average velocity, but in cases involving direction changes, average speed exceeds average velocity. Instantaneous speed is always equal to the magnitude of instantaneous velocity, as both are defined similarly at a specific moment. The discussion also touches on complex mathematical concepts, such as pathological functions, which can illustrate scenarios where average speed and average velocity diverge.