Yes, at least in Argentina, "Tanos" and "Gringos" stand for "Italians".
I heard once that "Tanos" comes from the last part of the word 'napoletanos' (naturals from Naples), not that every Italian immigrant came to the country from that city, but probably that's what many claimed they were coming from because it was one of the main ports back then, and popular use shortened the word afterwards.

Gringo, in Argentina, has always been synonym of Italian (that was my Dad's nickname), however in the past 25 years with the innovations in telecommunications and people traveling more and more, "gringo" was also incorporated with the meaning it has in the rest of America. But the most common for Americans is 'Yanki' and it is not a derogatory term, unless followed by a remark <g>.