Let us say I have two dedicated machines that I want to use for training. That means I want world_size=2. Then both min and max should be exactly 2 for the intended allocation, right? In what kind of scenario one would want to set min/max differently to take advantage of this flexibility?

If you have 2 machines you can use for training, then set the max to 2. If you are willing to start training with 1 machine, then setting min to 1 makes sense. You can set min to a different value than max when you are willing to start a training job with less machines due to faults in the system.
cc @cbalioglu