In my homebrew, one of the things that I defined but which never really came up in play was that sorcerers were basically "primative magic" and wizards were "advanced magic".
Sorcerers were basically people who were born with a natural ability to use magic that would manifest as they grew up. They'd work out how to do things with it (or not, as the case may be) pretty much by trial and error but didn't really understand what they were doing or how it worked. They just knew that they'd worked out a few tricks where if they did this and that and the other thing while holding such and such, a magical effect would happen. For thousands of years, this was pretty much the only kind of arcane caster around . You had to be born with the talent to become one and you pretty much just had to muddle through to learn how to do anything.
Eventually, a particular civlization arose that had philosophers who studied things to see how they worked in the same way Greek philosophers in our world studied various things. Some of them turned their attention to magic and, over the course of centuries, they worked out how magic actually functioned and what the sorcerers were actually doing to make various things happen. This let them create a codified system of "laws of magic" that defined how it all worked. They also figured out magic did not depend on innate talent and that anyone with sufficient intelligence and mental discipline could understand how magic functioned well enough to create magical effects. This, in turn, led to them working out how to be a wizard.
Thus, essentially, sorcerers practice "primative" magic while wizards practice "advanced" magic. Sorcerers magic is inborn and pretty much worked out by trial and error for each sorcerer. Wizards do not necessarily have any inborn talent but but do have a codified system of magic and centuries of accumulated magical knowledge to call upon.
That pretty much explains the differences between the two classes, as well. Sorcerers have an innate talent and can manifest more effects than a wizard of equal level, but their understanding of magic is so poor that they can only do a few things. Wizards, on the other hand, are basically working without the talent of the sorcerer and thus can do fewer effects than an equal level sorcerer and must impress them on their mind (memorize) instead of just doing them -- but their greater understanding of magic allows them to be more versatile than the sorcerer can ever be.
Sorcerers can attempt to apply some of the codified knowledge of magic to their own talent. I never worked out the details but this was basically the explanation for being able to take various feats expanding their spell slots or known spells and so-forth. One aspect of this was going to be that there was only a certain amount of this they could apply to their innate talent and, beyond that, they were studying to become wizards. This is because they both work differently. Wizards and sorcerers both manipulate magic, but the mechanism they use to do so is not the same (as manifested in game mechanics by wizards being dependant on INT and sorcerers on CHA). A sorcerer can use magical knowledge to make his own manipulation of magic more efficient but beyond a certain point he just has to leave his talent behind and learn how to do things "the wizard way". I had planned to have people who were sorcerer/wizards who had basically manifested a talent and taken it however far before they basically took up wizardry. A typical backstory there would be the kid from a remote village who manifested a talent and had a couple of levels of sorcerer before "getting noticed" and becoming an apprentice wizard.
That was probably too long winded. Sorry.