There are three kinds of spellcasters – internal, external, and other (a mix of both, or who draw their power from sources other than something like the Weave or the Force). Sorcerers are internal – they gain their power through an innate connection with the Weave, whereas wizards have to learn how to tap into their source of power (making them external casters).
Sorcerers are "free" casters - cast spells by manipulating raw magical energy. They don't need foci like wizards (Eschew Material Components), and they have the finesse of wizards, but they have more power (which translates into a greater number of slots) and the ability to draw upon that power to cast spells on the fly. They have an innate, "always-open" link with the Weave, which enables them to change the spell as it is being cast – effectively, they can add metamagic, alter the spell's appearance, etc.
The wizard, OTOH, is a "structured" caster - he has to forge a temporary link with the Weave and imprint the spells into his memory via an external focus (his spellbook), drawing just enough power to be able to cast each spell. When he casts them, they are immutable – he only has enough power to cast them the way they were imprinted. Anyone can become a wizard, if he is intelligent enough to understand magical theory and can hold the spells' energy in his mind.
After writing the bit about the sorcerer, I can see a reason for their having an increased time to cast metamagic spells – they have to draw extra energy and shape the spell as it's being cast, whereas the wizard has it prepped that way – all he has to do is speak the words, wave his hands, and presto. This would suggest, though, that higher-level sorcerers would be able to manipulate this energy more easily – extensive practice, coupled with increased (will)power and the ability to control to control greater amounts of magical energy. Say, a 10th-level sorcerer can cast metamagicked spells at normal casting time, rather than a full-round. Casting quickened spells as free actions might be possible in this scenario, but costly – effectively, you're grabbing the energy faster than usual, which doesn't give much room for control – it could require a Concentration or possibly Spellcraft check, DC 15+level to avoid blowing the spell and suffering some sort of magical backlash.
So where does all this go? The fundamental difference between sorcerers and wizards is not the type of magic they use, or how they use it, but what they can do with it.
Wizards, being "structured" casters, have extensive knowledge of magical theory and what spells can be made to do. Obviously, this translates to their being able to learn and scribe more spells, but it also means that they can manipulate the energy to accomplish a wider range of effects, many of which require a very structured casting (creating some items, for instance, or changing someone else's form).
Sorcerers, being "free" casters, draw on raw, untamed magical energy and shape it to their will – it precludes fine manipulation, for the most part, but it makes them excellent "blaster mages" (see the note above about bards). They would be able to cast spells that:
Manipulate energy (Evocation and some Necromancy), impose the caster's upon another (Enchantment - one of the perks of being a Cha-based caster), manipulate light and shadow (Illusion), move themselves or another through space (summoning and teleportation effects), sense or dispel magical auras (some Divination and Abjuration spells), and create short-lived magical effects (wall spells, cloud spells, etc.). I'd also throw a few odd spells in there, like dismissal, repulsion, spell turning, etc. – ones that simulate the sorcerer's will protecting him or preventing another from doing something the sorcerer doesn't want him to.
They would not, however, be abe to cast spells that:
Manipulate matter (but not energy) on a molecular level (most Transmutation effects), create (semi-)permanent items from nothing (most Conjuration (creation) effects), cast spells that gather information (legend lore, vision, etc.), cast necromantic spells that don't involve energy (contagion, blindness/deafness, etc.), manipulate time, or spells that require extraordinary prep time (guards and wards, soulbind, Drawmi's instant summons) or a structured casting (symbols, sepia snake sigil, explosive runes).
Basically, what they'd lose is most transmutation and conjuration effects, divination, and necromancy, but in return, they gain the ability to use metamagic normally at a higher level.
(In our campaign world, sorcerers are also more susceptible to arcane burn, since they're channeling raw magical energy with less control. We also have rules for ritual casting and spellwebs – ritual casting is more structured, and hence the province of wizards, while a spellweb draws and shapes pure magical energy. A ritual increases the caster level of a spell, while a spellweb increases the power of the spell.)
