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For the purposes of this question, I'll be comparing Wizards and Sorcerers, ignoring Warlocks and Divine spellcasters.
So the main differences are that Sorcerers can cast anything they know so long as they have spell slots, whereas Wizards can only cast what they have prepared, even though they know more spells, again providing they have spell slots to prepare.
For example, Arcane Recovery says that you regain some spell slots, but it doesn't mention about spell preparation. So if you burn through all your spell slots, do you have to re-prepare you spells, or can you cast prepared spells repeatedly, like a Sorcerer can, only limited by spell slots? To reword that, can you cast a prepared spell as many times as you like so long as you have spell slots, or can you only cast a prepared spell once?
Note that prior to getting into 5e, my only other knowledge of D&D came from NWN2, based on 3.5e, so it might be that things worked differently then, or NWN2 works differently. In that game, you had to prepare the same spell multiple times if you wanted to cast it multiple times...