What is the difference?
Control systems generate an output based on some input, a set of tuning parameters, and a setpoint. One example is the heating/cooling thermostat in your home.

One of the more common control systems is called PID, for proportional, integral, and derivative.



The control system tries to keep the feedback value from the process as close to the set point as possible, without overshoot or undershoot.



In the past, control systems were completely implemented in hardware.  I have designed them using a separate op-amp for each term, P, I and D, and used potentiometers to control the coefficients.

Embedded computers are general purpose computing platforms that feature a microcontroller (CPU, memory, and I/O).  They are very general and can be used for anything from controlling a microwave to being the guts of your smart phone.

You can completely build a PID control system using an microcontroller.

One such use is a automobile cruise control.  I designed one of these using a Motorola 8-bit microcontroller (HC05 for those that member) about 25 years ago.

So an embedded system is a general purpose (but small) computer, and a control system is a very special piece of hardware (or firmware, implemented in as an embedded system).

As far as a career choice, control systems would be a very narrow field.  Embedded systems would be much more general, probably more interesting, and if you want, you could still built a control system using a microcontroller.