Audio is what you hear. It is sound. Audio is music, dialog in movies, and commentators during the game. When we say we are experts in audio, it means we make sure everything you hear sounds the best it possibly can.
Audio is what you see. It is visual. Video is what you see in a movie, on a television show, or on your computer screen. When we say we are experts in video, it means we make sure everything you see on any screen is reproduced the way it is meant to be.
Video distribution is using various technologies to send video from one place to another. It can involve transmission of one source or many sources to one display or many displays. An example of video distribution is the ability to show many different tv channels on multiple televisions in a restaurant.