The part of the lamp that connects into the lamp holder of the light fitting is generally known as the Lamp "Cap", or "Base". There is a large variety of different types of Caps and Bases. Shown below are just a few of these different types of caps or bases to help you with identification.

This Bayonet lamp holder base is known as a 3 Pin BC and or B22d-3. It is not a common base, but was used in electric glow type fires fitted with fire glow light bulbs. They are now also used in new houses were the low energy saving pendant lamp holder are being fitted. The diameter of the base is approximately 27mm.
This Bayonet lamp holder base is known as a 2 Pin BC and or B22d. It is a very common in the UK. Most light fitting, table lights and the pendant drops are fitted with this type of base. The diameter of the base is approximately 27mm.
This Bayonet lamp holder base is known as a 2 Pin SBC and or B15d. It is not as common in the UK as the larger BC base. This lamp base is used where the size of the light bulb is required to be small. It can be found in Ceiling light fittings, small table lights, and small appliances etc. The diameter of the base is approximately 17mm.
This Edison lamp holder base is known as a Giant screw GES and or E39. It is not used normally used within the household. This lamp base is more commonly used in outside street light fittings etc. The diameter of the base is approximately 39mm.
This Edison lamp holder base is known as a large screw ES and or E27. It is more common in the US and Europe. It is more commonly used in outside light fittings. It can also be found in fans lights etc. The diameter of the base is approximately 27mm.
This Edison lamp holder base is known as a small screw SES and or E14. It is becoming more common in the UK. This base is used where the size of the bulb is required to be small. It can be found in light fittings where the shade is small in size. It is also used in refrigerators, sowing machines etc. The diameter of the base is approximately 17mm