There's four basic types of casters:
Full Casters: Bards, Clerics, Druids, Sorcerers, Wizards
Half Casters: Paladins, Rangers (Artificers?)
Third Casters: Eldritch Knights, Arcane Trickster (Artificers?)
Pact Magic: Warlocks.
Full, Half, and Third casters basically use the same chart, just do the appropriate math. (a 6th level third caster is equal to 2nd level full caster. A 6th level half caster is equal to a 3rd level full caster)
Warlocks do their own thing. They get a small selection of spell slots (2 slots up until 11th level unless you have equipment that give you extra slots) that recover on short rest instead of full rest.