A wizard isn't just some man who read any given book.
A wizard didn't do a "deal with some patron.
A wizard isn't begging some eldritch being to borrow power.
A wizard is researching the arcane code that makes the weave work. Those books are what software engineers call "the documentation".
If the Sorcerer is using their god to exploit the weave, they have no fucking idea how any of it works, they just ask their patron to make things happen and are revealed arcane secrets through dedication to their god, a wizard is openly hacking the fabric of reality by reading the documented accounts of those who came before him, and using that arcane wizardry to bend the slivers of the exposed weave to their will.
A sorcerers power comes from their Patron, a Wizards power comes from the sheer force of their will, their determination to uncover the mysteries behind how the arcane works.
A wizard might one day stumble on the secret to unlocking 10th level magic and beyond, a sorcerer is bound by what their patron is allowed to thread through the weave.