As lismuscionico already said, the Poldina is the original. You can probably choose more light variants and the charging method is certainly different. With Poldina, you don't have to plug in a cable, just place the lamp on the contact plate.

I am not familiar with Coop's product. But it is not the same brand: the company that makes the Poldina is called Zafferano (not Luminart). So it is not the same luminaire.
I would also point out that there are many similar lamps on the market. I have never bought them and do not know if they have the same quality and similar (or perhaps superior) performance. However, the original is Poldina: it was the first battery-operated lamp produced with this shape / material / charging technology.