What is the difference between a sampled time system and a discrete time system? I am trying to evaluate whether I should control a system in simulink using sampled data system or discrete time system.

The discrete model is as follows: 


The sampled time system is as follows


What is the functional difference between these two and which approach is preferred in realistic modelling and control?
The first one is a purely discrete model. You need to select a discrete solver in the simulation options to accurately simulate this system. The second system however is actually continuous because of the holders, so you need a continuous time solver.

The preferred approach depends on what your system is. If you have a discrete model to work on, you should prefer the first one. If you have an actual physical system that you want to control with a microcontroller, you should prefer the second one.