I mean, I was pretty clearly speaking mechanically. Every Wizard is going to be pretty much the same, mechanically. Once you pick a subclass of, say, Fighter? Things will be pretty much the same, mechanically. There are ten Fighter subclasses (and some of them...are really pretty bad. Like Banneret.)
You can attach whatever story to that you want. Many Wizards could just as easily be played as Artificers, or Bards/Sorcerers with good Intelligence, etc. Hence, mechanically, there's only a handful of stories. You've always been able to invent whatever story you want that has zero impact on mechanics. Nothing about that has changed.