Many get very confused with this.

 

All modulation types are defined by the pivot chord (the chord that belongs to both keys and enables the modulation), not by the key the progression goes to. The different “types” of modulation consist of different functional roles assigned to the pivot chord—this is where function theory explains the process more clearly than a purely scale‑ or degree‑based theory of tonality.

This is why theorists gave modulation types specific names: the pivot chord is the essence of the modulation, not only the destination key. The task of a theory is to provide short, clear terms that make musical argumentation precise and easy to remember; the task of a good book or lesson is to give you a clear definition.

The term “dominant” can also be conceptually misleading if you examine it closely. But that’s a separate topic.