No, The light emitting part is a lamp, it really is!
However, since the introduction of the electric light ‘bulb’ common usage has used the word bulb to mean lamp. I'm probably a bit longer in the tooth than you Nigel, so I come from an era when the pros used the word lamp, while the general public used the word bulb. The word for what a lamp fits into is a ‘fitting’ or ‘lamp holder’.
This is not very important in the scheme of things, so if you like to say bulb, then fine & dandy. If you are keen to be right, then please accept my apologies, you are right & I am wrong, that is fine too.
Peace,
Pat.