What is a "discrete time controller"?
Continuous time is the world we live in - something can happen at any time, 1 second? 1.1 seconds? 1.111111111111 seconds?. Your plant will exist in real time - e.g. a motor speed would be continously changing and not changing at discrete time intervals. Control systems have to interact with this world somehow.
If your entire control system was built using an analogue circuit with no sampling, then it would be a continuous time controller. As the environment changes, so does the output of the controller.
Digital systems however, don't work like that. You have typically ADCs to measure changes in your processes - what is the motor speed, what temperature is the chocolate, etc. ADCs sample the analogue signal into discrete time steps - you know what happens at t = 0, t = 1/sampleRate, t = 2/sampleRate, but you don't know what happened at t = 0.5/sampleRate. All of you control is now performed on these discrete time steps - you have a discrete time controller.