Yes, we fill out different landing documents for the USA and ,many other stations around the world. There are also many places (Oz for eg) where your normal pax would require a visa but, we don't (when operating as crew).
Also, it's quite rare for our passports to be stamped. I think this stems from the days when it was difficult to travel with a SA stamp or an Isreali stamp if going to the Middle East. I could be wrong, maybe its just that our passports would soon run out of space!!!