DND was a kind of setting, and there were quite a few worlds with similar settings.
And Red Robe Wizards were members of the Red Robe Wizard Society of Thay, which meant this was Faerûn.
The mages of that world were subject to something called Spell Slots.
Though it couldn't exactly be called a restriction, because the Weave and Spell Slots actually lowered the difficulty of learning and casting spells. They were more like tools.
As for those powerful Legendary Mages, many had ways to bypass the restrictions of Spell Slots. There were also extraordinary things like Legendary Spells, which were no weaker than the mages of other worlds. They were even much stronger! After all, many mages in that world had successfully become gods! By their standards, the vast majority of wizards in the magical world were sorcerers.
Only those who learned and researched magic, mastering all its information and details, counted as wizards.
Those who relied on instinct and inherited bloodlines were sorcerers.
Wizards were born with magical bloodlines, so they were undoubtedly sorcerers.
It was just that many famous wizards in the magical world were also scholars and researchers, people like Dumbledore. So they were both wizards and sorcerers.
In DND worlds, a wizard's upper limit depended on Intelligence, while a sorcerer's upper limit depended on bloodline.
Take the High Arcanists of Netheril. The lowest Intelligence among them was 17, and that was considered terribly poor aptitude.
The renowned High Arcanists all had Intelligence above 20—22 to 24, for instance.
By modern Muggle intelligence testing standards, normal people scored between 90 and 110.
A score of 120 to 140 meant you could be called smart, while anything above 140 made you a genius. The higher the score, the smarter you were, and the maximum score was 200.