Classifications and grading systems for diabetic foot

What are various types of Diabetic feet?
Following are the 3 types:

Neuropathic Foot: Neuropathy dominates. Fissures, bullae, neuropathic joints and edema, digital necrosis.
Neuroischemic Foot: Occlusive vascular disease main factor while neuropathy is also present. Rest pain, foot margin ulceration, digital necrosis and gangrene.
Non neuroischemic foot: No significant neuropathy or ischemia. Secondary to trauma. Infected because of uncontrolled, often undetected diabetes

What are various systems of grading of a diabetic foot?

Wagner 's Diabetic Foot Grading System
University of Texas Wound Classification System
PEDIS Ulcer classification system