So like the entire spirit and national identity of Portugal is just "we're not Spanish".

Can't speak to the country today -- never quite made it back to my grandparents' roots. But from growing up Portuguese in a significant Latino culture, I would say there are differences reflected, to begin with, that former Portuguese colonial descendants tend to embrace their Portuguese heritage while Latino's look upon the Spanish as invaders and marauders who tried to steal their wealth and destroy their native cultures. In my experience, Portuguese descendants tend to keep their emotions more internalized, have assimilated more with the local populaces whereever they have gone (which is everywhere except Antarctica, and at the same time spread parts of their various colonial cultures across their entire former Empire. Their music is different (the fada is far more melancholy than most Spanish music) and the food is different. Back in the 60's when stationed in Europe a barracks mate of mine and I travelled to Madrid because we were hungry for Mexican food -- well, Cal-Mex -- and the only Mexican restaurants in Europe at that time were in Madrid. Significantly, both were founded and owned by a retired U.S. Navy NCO. And were next to each other.

They don’t even speak Spanish, what are you talking about?