The element linking the final control element and the measurement is the controller. The controllers are usually single loop PID controllers before the advent of computers. These are manufactures to execute PID control functions. These days the controllers can do a lot more, easily to 80 to 90% of the controllers are still PID controllers.
It is difficult to say that controllers of analogue are definitely better than digital controller. The controllers of analogue are based on mechanical parts that cause changes to the process via the final control element. These moving parts are subjected to wear and tear over time that causes the response of the process to be somewhat different with time, again like final control elements. Analogue controllers continuously control.
Digital controllers do not have mechanical moving parts. Instead the use processors to calculate the output based on the measured values. Since they do not have moving parts, they are not susceptible to deterioration with time. Digital controllers are not continuously control. They execute at very high frequencies, usually 2-3 times per second.
The controllers of analogue should not be confused with pneumatic controllers. Just because a controller is analogue does not it is pneumatic. Pneumatic controllers are those that use air instrument to pass measurement and controller signals. Electronic controllers have the advantage of not having the same amount of dead time and lag due to the compressibility of the instrument compared to pneumatic controllers.
The DCS is a control system which collects the data from the field and decides what to do with them. Data from the field can either be stored for used for simple process control, future reference, and use in conjunction with data from another part of the plant for strategies of advance control. The DCS is involving of Engineering station, history module, data historian, control modules, input and output.