This answer on Quora really has some detail and should answer your question. Very well written !
What is the difference between a mage, a sorcerer and a ...
In gaming, what is the difference between a Mage, a Wizard, and a Sorcerer?
It depends on the game ... But in D&D, it mostly has to do with what spells they can cast and whether it is an ability they are born with or something they have to learn ... And use a spellbook or memorize spells.
There is also a difference between classes that use arcane magic (such as those you list), and classes that use divine magic (such as clerics).