The Cuban sandwiches I had in Florida were made with a device, sort of like a waffle iron, which squeezed and heated the sandwich. Most of the “Cuban” sandwiches I have had in California don’t use such a device.
On a visit to Florida a few years ago, I stopped at an eatery and had a Cuban sandwich and told the proprietor that now I knew I was in Florida because I was eating a real Cuban sandwich.
Outside FL (or Cuba), the key is never order a Cuban sandwich if you are not in a legit Cuban restaurant. Anywhere else, you will get the cook's "interpretation" of a Cuban. Finding a good Cuban restaurant in CA can be almost as challenging as finding a good delicatessen. Most here are no better than your supermarket deli and use the same vac-bag meats.
I don't know if paninis belong anywhere specifically in the US, but they often are burnt on the outside and still cold on the inside. Bread is too good an insulator for those waffle irons.