A good goal to have is for the DynamicModule to be self-contained, depending only on things in the system that essentially don't change. The point of Initialization is that when the kernel starts up, stepOnce[] is not defined. If the DynamicModule[] is displayed when someone opens the notebook, the Front End will start running the module before the user has a chance to define stepOnce[]. The Front End will run the Initialization before running the body of the module. If stepOnce[] is defined there, you can be sure it will always be defined in any instance of a module. I'd recommend Initialization over the option SaveDefinitions -> True, but you could look that up. It figures out the initialization automatically, but sometimes one is surprised by what it did.

The use of ClearAll[stepOnce] is good practice when making definitions. The thing to remember is that func[...] := value adds a definition rule to the list of definitions for func (DownValues[func]). The addition will replace an old definition if the patterns on the left of the := are equivalent, but any previous definitions that areare not equivalent will remain and could cause trouble. The same considerations apply to clearing attributes, etc.

Personally, I would use the localized version. The definition does not use much memory or take much time. Sometimes different dynamic modules need access to the same global resources. Then the global version might be a helpful example. Bulletproofing this can be more work than it's worth. At the least, you need to make sure that the global resources are defined and available before your modules try to use them.

Here's a fix;

DynamicModule[{t = 0, slider = 0, stepOnce},
 stepOnce[] := (t++;);
 Column[{
   Grid[{{"Slider", 
      Slider[Dynamic[slider], {0, 1}, ContinuousAction -> False], 
      Dynamic@NumberForm[slider, {4, 2}]}}, Alignment -> Left, 
    Spacings -> {2, 1}],
   Dynamic[
    Refresh[stepOnce[];
     Row[{"t = ", t}], UpdateInterval -> 2, TrackedSymbols :> {}]]
   }
  ]
 ]

If I can find the time, I'll explain later. It's complicated.

This is exactly what I need. Thank you. If find the logic of DynamicModule quite unclear.