Chat usually refers to a small group of people, or even just 2 people, with similar interests. Communication is much bigger, with endless possibilities and descriptions. For example - talking, teaching, learning, internet, body language, facial expressions, writing, reading, tv, radio...the list is endless

Communication is an umbrella term for all forms of contact. Whether it be spoken, written, smoke signals, morse code etc. It can be any kind of sending and receiving of messages from one person to another, informal or formal. Chat has a more informal tone and implies face to face conversation or talking on the phone, though it does not strictly mean spoken out loud you could also text chat online via a messenger like facebook for example.

Communication means, in a simple way, passing information from one person to another. You can communicate through writing a letter, an email, speaking, sign language, chat and so on. Chat means to write messages through a Facebook, Skype, Whatsapp chat box or it can mean talking to someone about simple day to day activities.