There's many variations and everyone mix their soil a bit differently. From what I understand Turface and pumice are interchangeable, but they're different from grit because they hold a bit of moisture while creating air pockets, but grit is just for drainage.
Please correct if I'm wrong!

No, turface and pumice are not the same. They have different properties and are not interchangable. Tueface is calcined clay and holds quite a bite of water. Pumice is a volcanic rock that drains quickly and provides a very good air tobwater ratio. You can grow plants in straight pumice that would drown very quickly in straight turface gravel has fast drainage and without the internat pore space of pumice holds even less water. It also has a much greater bulk density which can be useful for designing container soils for high wind areas.

Thanks for clarifying that for me.