Technically, this is true in English as well. But unless one is speaking to an electrical engineer, almost everyone refers to a lamp fixture as "a lamp".
If one searches images one will see that 'φωτιστικό επιτραπέζιο' or 'λάμπα επιτραπέζιο' give very similar results. One can also use 'πάτωματος'. A general (not image) search for table and floor lamps shows that 'λάμπα' yields about half as many hits as 'φωτιστικό'. For table lamps about 4.5 million opposed to 8.6 million. So while 'φωτιστικό' is preferred, it is quite common to use 'λάμπα'.
On the other hand, an image search for just 'λάμπα' shows pages of light bulbs while a search on the English term "lamp" shows pages of table and floor lamps (not bulbs). So there is a real difference between Greek and English usage of lamp/λάμπα, but λάμπα does mean what English speakers understand by "lamp" when qualified by one of the adjective nouns '"table" or "floor".
In objects from section 3 you get :-
Write “the lamp” in Greek Correct solution: η λάμπα
where φωτιστικό is rejected as an incorrect answer. In another section the same (or close) question rejects λάμπα and insists on φωτιστικό. This has left me totally confused as to the correct usage.