Online chat is a generic term for what are now mostly known as instant messaging applications - computer programs that enable two-way typing to connect users to each other.
However, there are net dating systems and other online services that do not use these applications to provide chat facilities, e.g. Delphi, often relying on HTTP-based protocols instead. Sometimes these are called a chat room or chat page extending the physical metaphors of 'sites' and 'magazines' which many web services exploit.
Some of these systems also provide telephone voice mail access. These are usually known generically as just chat systems.
The earliest online chat system widely used was probably the Unix talk facility. The earliest one in general use was likely the French Minitel. The concept took off with the Internet Relay Chat (IRC) protocol, which is considered an instant messaging tool.