What is the difference between Chats and Incoming chats in stats?

Incoming chats are the chats initiated by website visitors by clicking on a chat button.
Chats are all incoming chats and invitations together. 
LiveAgent can initiate invitations automatically (based on the setting of your invitation(s)) and when the website visitor accepts the invitation it is counted as a chat. 
An agent can also initiate an invitation from the agent panel and it is counted as chat.
In addition, if 2 agents join the same chat initiated by a customer, then it is counted as 1 incoming chat, but 2 chats.