IIRC, wizards in 3e could cast the same spell more than once too. They just had to use up more of their daily allotment of spells per day (so less variety in spells for that day). I don't recall there ever being a rule that wizards could only cast each spell once.
The main difference I recall for sorcerers was that all of their spells shared the same pool of resources, so they didn't have to specifically prepare which spells they wanted to use ahead of time. So while a wizard with 4 level 3 spells per day would have to choose at the start of the day (for example) whether they wanted to cast dispel magic 1, 2, 3, or 4 times (at the expense of using other spells of the same level) a sorcerer could use whichever 3rd level spell they wanted to at the time of casting until they ran out of their allotment of 3rd level spells. Which is why they called it "spontaneous casting." Sorcerers also got fewer spells overall, though their flexibility in casting was supposed to make up for that.