Ayumi Ashi=basic step. This appears to be the typical foot work used in many styles of karate where one slides the back foot up to the front foot and then steps forward (sort of a zig zag). Aikido calls this "walking" except the toes are pointed outward.
Tsugi Ashi=sliding step or shuffle step by sliding the back foot up to the front foot tand then step forward on the front foot without chaning hanmi.
Okuri Ashi=sending step=the only difference I can see on page 29 of New Aikido is the stance is a little wider with the step up.
TENKAI ASHI=pivot, pivot on the feet so you face 180 in the opposite direction (Aikido) New aikido seems to put this in the body movement category which is just referred to as sabaki (tai sabaki in Aikido).
KAITEN ASHI=step forward and then pivot 180 degrees (Aikido)-no definition in New Aikido.
TENKAI ASHI=pivot from one hanmi to the opposite hanmi or oblique stance (Aikido). Called a revoling turn (Tenkai) in New Aikido and is in the body movement category as a revolving turn-this is the turn from kaitennage (uchi version).
TENKAN ASHI=pivot with back step (Aikido). Just called TENKAN in New Aikido and is a body movement. When practicing with a partner it becomes TAI NO TENKAN HO (body turning) (Aikido) and Katate-dori Tenkan (New Aikido).
TENSHIN=sweeping body movement. This is the movement of yokomenuchi shihonage where you step to the inside and switch feet