DP stands for Decentralized Peripherie, meanin this is used to get and ssend info to the outside world by means of sensors and actuators. In other words: your input and output cards are not located in the PLC-rack but remotely. This is used to simplify cabling, because only a 2-wire cable is needed instead of N wires depending on the nuber of ins and outs.
FMS means Field Messaging System and is used for inter-PLC communication. It therefor has nothing to do with inputs and outputs directly, but everything with internal data from the processor.
I believe there even is a third version of Profibus, namely PA or Plant Automation. This is somewhat less used, because it's used for communication between PLC's and computers. The size of data being transported is bigger than with FMS.
Hello Jean-Pierre:
Your description of DP and FMS is basically correct:
DP is RS-485 based, master-slave cyclic protocol;
FMS is RS-485 based, master-master acyclic protocol.
However, Profibus PA is a sub-net of Profibus-DP, used to communicate with field process transmitters (level, pressure, temperature) and Ex-zones. Basically it is a digital version of HART communications.