I brought home a few twigs, only to discover they dry up too fast to do a good study. And to learn that is why you have to bring your olives to the oil-mill within days of picking.
Here are the two species we picked. I know the top one is called rosciola, due to its reddish hue, I presume (rosso = red). I don't know about the bottom one, not surprising, giving there are about 500 autochthonous species in Italy.