Anyway, before I get into old man ramble mode, I wouldn't mind getting different viewpoints on what 5e Sorcerers and Bards really are, and, specifically, why they're not just the "budget Wizards" that my brain insists they are.
Sorcerer is Wizard but with metamagic. What a Sorcerer lacks in their number of learned spells, they make up for with their ability to adjust spells with metamagics (You might be aware of metamagics being a optional feat for any caster in prior editions. In 5e only Sorcerer gets them)
Thus a Sorcerer can do things like twin a spell to cast it on 2 different targets, or haste a spell to cast it as a bonus action. Or even extend a cast to turn a melee touch spell into a ranged one allowing its safe usage.
Sorcerers are more adept at throwing out a lot of power in a short amount of time than any Wizard. Between things like Twinned Haste to speed up 2 party members, to double casting big powerful spells by hasting one into a bonus action. While a Wizard favours having access to more spells and the ability to swap out available spells at a moments notice.
As far as Bard goes, it's more of a Gish style class. That can mix in some physical attacks alongside their spells which tend to be more support orientated - Buffing aliies and debuffing or controlling enemies than outright damage. With exception of their Magical Secrets which allows them to access a spell from ANY other caster which can allow them to access some rather powerful damaging spells. They also get their class resource of Inspirations, which allows them to do things like give an ally a bonus on rolls, give an enemy a malus on rolls or turn them into potent attacks to use with melee or ranged weapons. Bards also get bonuses to their skills in the form of expertise, much like a Rogue and also has every single skill available as a class skill.
In both cases, Sorcerer and Bard also utilize CHR as their spell casting stat, which also means they excel at being a Face for the party (The one who talks to everyone and can use Persuasion, Intimidation and Performance skills to manipulate dialogues)
