The base is the same as a halogen bulb, but a HID bulb is actually a burner, with two cathodes that ignite a gas in the center. It's longer and thinner than a halogen bulb, and as a halogen headlamp (reflectors) are designed to work with the shape of the bulb, it can throw the pattern off if the bulb is of a different shape.
Hence why it blurs the pattern, and causes glare. A projector has a shield that just cuts off whatever light is above the pattern, so it doesn't matter about the bulb shape.
And yeah, PjMetalHead is right with the adapter - the HID bulbs don't fit into the standard ones as the wires are fixed permanently to the base of the HID bulbs. The HID equivalent holders are only about £8