Kinesiology is the comprehensive study, or science, of the physical body undergoing movement and exercise and doing physical work. But also included in that study would be anatomy and physiology, biochemistry, and nutrition. Also injury prevention and treatment.
Biomechanics is much more focused and limited, concerning itself almost solely to the type of movements and form, technique, required to perform an exercise. It is similar in that fashion to a mechanical engineer studying the movement of a machine.
Biomechanics would be something that would be studied in Kinesiology. In other words, it’s a sub-discipline.