As you've been told, Modbus is a protocol, originally developed by Modicon and released to the public domain.
There is actually a family of Modbus protocols now. The original public domain Modbus is technically Modbus RTU. It has several variants, ASCII and Hex, for example. When the term "Modbus" is used without modifier Modbus RTU is what is meant. It is a master/slave architecture, and is probably the most widely used communications protocol, and most PLC and HMI brands will support Modbus. It is used widely to connect devices from many different manufacturers.
There is also Modbus Plus, which is a peer to peer protocol and still proprietary for Modicon. There is also Modbus over ethernet, which is widely used.