What is the difference between control engineering and instrument control?

the job of the control engineer is to control the instrumentation

control engineering is related to build a project where we can configer all instrument systems such as DCs and PLC and interface it with filed device and measure,indicate,logging and control them from remote area.
instrument control is spesific related to instrument loops which have primory sensor ,controllers and final control element.

control engineer is the one who make the control circuit which is the connection between instruments and electrical components and plc or any other type of control instrument engineer work on electrical instruments

Control engineers are expected to have more mathematical capability.
e.g., the essentials of control system theory, sample-data systems, optimal control systems, self-adapting controls and so forth.
Instrumentation and control engineers are typically employed to monitor, measure, regulate and control physical quantities like temperature, pressure and flow, and to control product movement, actuators and positioning devices for example, in a range of modern industrial and production setting including Oil&Energy, manufacturing, environmental, health, food production, mining etc.

Control engineering represented the all components in control room in production units such as Power supply card PS and central processing uint CPU for DCS system or PLC system as well as another cards.
Instrument control represented the all instrument devices in field such as: Pressure transmitter, Flow, Temperature and Level transmitter as well as Control valve and Pressure switch...etc.