Crutches
These are used by placing the pads under the armpits and holding the grip, which is below and parallel to the armpit pad. These are sometimes known as axillary crutches.
Forearm Crutches
These are used by slipping the arm into a cuff and holding the grip.
Platform crutches
Used by those with poor hand grip (due to arthritis, cerebral palsy, etc.). The arm rests on a horizontal platform and is strapped in place.