To add to that, the player with the mod may be more limited in the scope of what they can do whereas the player with the cheat console has many more options depending on what codes they type. The trade off is ease of use versus depth of knowledge. 

And to add to what I said about Wizards having no inborn magic, it's important to note that some races do have inborn abilities independent of their class, such as a Dragonborn's breath weapon, for example.