Magical Sources

This article details the sources of power of all the playable magical classes for DnD, including those from the Valda's Spire of Secrets add-on.
Links: Wizardry, Soul Arts   For example, if you are playing a sorcerer, who's source of power is "Often Soul Arts, can be anything", that means you could have your character be a powerful user of the soul arts, specialised into a certain type dependant on subclass, or you could be gifted from birth with magic from another source, such as a deity or other powerful connection.
The soul arts are naturally chaotic and non-distinct, taking on many forms.   General rule of thumb, if a class, subclass or feature uses your Intelligence modifier for a magical effect, it is probably Wizardry; if it doesn't use Intelligence, it can't be Wizardry.  

Official

Artificer: Exclusively Wizardry.
Bard: Often Soul Arts, but can be other things.
Cleric: Exclusively Soul Arts.
Druid: Can be anything, similar to Warlocks. Most often a reward for servitude to Roc, the Scribe of Beasts.
Monk: Exclusively Soul Arts.
Paladin: Often Soul Arts, but is much looser than Clerics.
Ranger: Can be anything.
Sorcerer: Often Soul Arts, can be anything.
Warlock: Can be anything.
Wizard: Exclusively Wizardry.
  Blood Hunter: Can be anything, including Wizardry.
 

Magical Subclasses

Barbarian: Mostly Soul Arts, but can be other things.
Fighter, Eldritch Knight & Arcane Archer: Exclusively Wizardry.
Other Fighters: Can be anything.
Rogue, Arcane Trickster: Exclusively Wizardry.
Other Rogues: Can be anything.
 

Valda's

Alchemist: Exclusively Wizardry.
Investigator: Mix of both Wizardry and Soul Arts.
Martyr: Can be anything, similar to Warlocks.
Necromancer: Exclusively Wizardry.
Warden: Can be anything.
Warmage: Exclusively Wizardry.
Witch: Exclusively from a curse given by Izall, the Scribe of Curses.