It’s not straight forward, but basically if you use a plastic lampholder it’s a 2 core flex and if you use a metal lampholder it’s a 3 core flex.

It’s all to do with the need for any earthing on the lamp.

So if you want to use a plastic lampholder, but there is the need to earth any part of the lamp, then you will need a 3 core and ensure the earth is connected to cover any requirements. Some plastic lampholders can be purchased with an earth terminal in the base.

Also, there are lamp designs that are metal but have a plastic lampholder fitted. If there is a safe route for the flex with no potential for damage, then a 2 core flex can be used to supply the plastic fitted lampholder. However, in this case an isolator must be used in the base of the lampholder to ensure there is plenty of isolation to the metal parts of the lamp base.

Don’t forget, the earth is there for safety reasons, so if needed then please ensure it’s connected.