A wedge base is a type of electrical connector used as a fitting for small light bulbs. It is similar to the bi-pin connector, except that the two "pins" are the same wires that extend into the bulb, and the wires are bent up onto the sides of the base, where they make contact with the socket. The wires are usually inserted into a plastic base that the bulb is mounted in, and which is often narrower at the tip than at the bulb, giving it a wedge shape and usually ensuring a tight connection, depending on manufacturing tolerances. Some bulbs have no plastic base, and the wires are simply bent up to the sides of the bulb's glass base.
W2.1x9.5d base, a common 5-watt bulb in landscape lighting and some interior automotive applications such as the dome light
5mm dome LEDs with wedge bases and locking tabs
W2.1x9.5d base (as in the image at the head of the article), but 16 watts for automotive use
W2.5x16q base, 7- & 27-watt filaments for parking lights and brake lights, will also fit WX socket for turn signals (legal only with amber covers)
A bipin or bi-pin is a type of lamp fitting. They are included in the IEC standard "IEC 60061 Lamp caps and holders together with gauges for the control of interchangeability and safety". They are used on many small incandescent light bulbs, and for starters on some types of fluorescent lights.
A metal halide lamp with a bipin cap
Halogen lamps with GU4 (left) and G4 (right) bases
Halogen lamp with G6.35 base
Metal halide lamp with G8.5 base