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This question already has an answer here:

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...

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marked as duplicate by diego, Adam, András, Icyfire, Ceribia Apr 17 '17 at 20:01

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You can cast a prepared spell as many times as you like, as long as you have the spell slots.

From the description of wizard spellcasting, on PHB 114:

Casting the spell doesn’t remove it from your list of prepared spells.

I believe that this is a significant departure from 3.5.

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Wizards

Wizards have to prepare spells as detailed on page 114 of the PHB - a number of spells equal to their Wizard Level plus their Intelligence Modifier. These spells must be spread across every level the Wizard has spells for. They can then cast these spells using their spell slots. It doesn't matter how many times they cast each one, as long as they prepared the spell and they have a slot.

For example, if a wizard has prepared Shield and Magic Missile (among his other spells), and has four available spell first level slots, he could cast Shield four times, or Magic Missile four times, or any other combination of prepared spells up to four.

Arcane Recovery allows him to get a small number of spell slots back on a short rest. He does not get to change his prepared spells (that happens after a long rest), but can pick which spell slots come back based on what he's used and what he thinks he may need before he gets to rest again.

These spells have to come from his spell book. There are no limits to the number of spells he can put in his book, other than than having a supply of ink to do so and the size of the book.

Sorcerers

Sorcerers know a finite number of spells. They don't have to prepare them; you can consider them always prepared, if you like. They cast them the same way a wizard does, they just have fewer choices.

In 5E, Sorcerers are the only characters that have access to metamagic. They can modify their spells on the fly. In effect, they have less choice in what they can cast, but more flexibility in how those spells function.

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