Ankle Strap: Shoe with a strap that fastens around the ankle.
Ballet flat / pump: Flat shoes with rounded toes and thin soles like ballet shoes.
Court: Classic closed-toe shoe with medium or high heel could be pointed or round toe.
D’Orsay: Shoe with a closed toe and heel support, but missing the section in the middle.
Dancing shoes: Mid heel T-bar shoes, usually with a closed toe / ankle, as worn by ballroom dancers.
Dolly shoes: Similar to a Mary-Jane, with the strap set slightly higher on the foot. Round-toed.
Espadrille: Wedge shoe with a woven rope sole and a fabric upper (often with ankle ties).
Flat: Shoe with no heel or very low heel.
Flip-flop: Flat shoe with a bar that sits between the big and second toe.
Loafer: Shoe upper made in two parts, the top sewn onto the sides as a design detail.
Mary-Jane: Shoe with a small strap across the front of the foot.
Moccasin: (often suede) shoe similar to a loafer in style with more obvious stitching. Usually flat.
Mule: A slip-on shoe without any straps / ankle support.
Open-toe: Shoe with front section missing revealing all the toes.
Peep-toe: Shoe with a cut-out section at the front, revealing one or two toes.
Pilgrim shoe: Flat, pointed shoe with a buckle across the front.
Pump: Confusingly this term is used in UK to mean a flat cotton/elastic/rubber combination worn for PE lessons or Ballet pump but equally this term is being used more an more by shoe designers as another term for a Court shoe often sexy pointed toe high heels.
Sandal: Shoe with open toe and (usually) straps around the ankle / across the foot.
Slide: Similar to a flat mule, with just one piece of fabric over the foot.
Slingback: Shoe with a strap going round the heel.
Slipper: Slip-on shoes not designed to be worn outside.
T-bar: A shoe with an ankle strap that hooks into a strap running right up the foot creating a 'T' shape.
Thong: Another name for a toe-post / flip-flop. In the UK we tend to use this term regarding a form of underwear rather than shoes.
Toe-post: Another more trendy name given to a flip-flop. May have a heel / extra straps.
Trainer / Sneaker: Flat shoes generally with rubber sole and laces designed for sport.