What is the difference between "system" and "control volume"? I understand that we use the term 'control volume' for both open and closed systems because even though we can choose a fixed amount of mass in closed systems on which we base our calculations, we cannot do it for open systems. Thus we choose a control volume. What I do not understand is why do we add an extra term instead of just using the term 'system'.
 A: A control volume is quite a specific concept - a region of space inside some closed surface. Control volume is almost always of finite dimensions and with well defined boundary.
A system is a more general concept -  a set of objects, usually sharing some property. This property can be sharing the same closed region of space (closed system), but it does not have to be so. A system does not necessarily have obvious boundary surface ( e.g. a globular cluster, or a ferromagnetic body in external magnetic field), or it does, but not everything that is inside that surface is meant to belong to the system (e.g. set of water molecules in atmosphere inside a room).
A: The control volume can be a subset of the system and 'signals' that pass through the boundary treated as inputs or outputs. The control volume is that prt of the system that is under consideration; the part to be modeled.
A: An open system simply means mass can enter and exit the system. But if the mass flow rate into and out of the system is constant, then the amount of mass, at any given time, in the control volume is constant. 
Even though we can choose a fixed amount of mass in closed systems on which we base our calculations, we cannot do it for open systems.
We cannot do it for open systems simply because there is mass flowing into and out of the control volume, which makes it an open system. But if the mass flow rate is constant into and out of the control volume, then there is no build up or decrease in mass in the control volume.
A: Refer to this video I have made, Control Volume Video to understand the clear difference between system and control volume.
A: Field variables(Pressure, temperature etc) through Control Volume are the function of space and time,
Which implies Control volume method is Eulerian approch.
System let's say system volume which moves with the fluid, so field variable in system volume is function of time only,
And it is an lagrangian approach.
