What is the difference between profibus and modbus? What type of controller is used in dcs?

First question, Both are communication protocol design by different companies. Many companies these days are using both, and depends on the manufacture and the application it will be provide what suit your controller features..   

Second question, In Honeywell they use C300.

Modbus & Profibus are both application layer protocols. Modbus works on RS485 & TCP/IP whereas profibus works on only 485 control protocol. A Modbus network can have a master device and 247 slave devices. The profibus network can have a maximum of 126 devices in its network. Profibus DP is faster in speed as compared to Modbus. The Profibus DP speeds vary from a few KBps to 12 MBps.

Modbus is the most general protocol used in industrial protocol and can be used base on Ethernet and RS-485  or RS-232.

Profibus is a protocol used by Siemens automation systems and based on RS-485.