Toe shoes would qualify as barefoot too, but I they're just a more extreme version I think.

Barefoot shoes usually have 3 traits:

• Zero Drop - The shoe is the same height from the back to the front, so your heel isn't higher up than your toes
• Flexable, thin soles with no arch support - Allows you to feel the ground and build up strength in your feet and arches
• Wide toe box, to allow for your feet to retain their natural shape for comfort and stability.

This video does a good job of explaining why those other two traits are desirable.