Panino is Italian for sandwich, it literally means small bread.
Panini is something I first experienced in France, where it's made with a special semi-raw bread. I've never seen anything quite like it in Italy, though.
Panini and Panino are pretty much synonymous. Panini is just the anglicized word, although it seems the Italians don't generally grill them. I've had Panini/Panino in Italy, France, the UK, and Canada.
