Hemiplegia is the partial or total paralysis of one side of the body that results from disease of or injury to the motor centers of the brain. [Merriam-Webster’s Medical Dictionary]
By this definition, hemiplegia is not the same as facial droop or facial paralysis. Hemiplegia is the result of a disease or of an injury that affects the motor centers of the brain.
Partial facial droop is the result of extreme anger or a CVA, i.e., cerebrovascular accident, that affects only the nerves that control facial movement.
The locations of the nerves that control facial movement and the brain’s motor centers for body movement are located at different places in the brain.