If you’re backpacking across Europe, visiting friends, or just vacationing in a foreign country, you are a tourist.
If you’re studying abroad for a semester as part of your university (or your high school) education, then you are still a student, albeit a study abroad student.
If you are working in a country for a few week to a couple of months, but you’re maintaining a position at a remote office and you’re just on site to help, then you are on a business trip.
If you’re on a base and you cannot leave that base, and you’re living on home country style amenities (austere as they may be) then you’re deployed (yes, contractors too.)
If you’re living abroad, living off of the economy, and you’re there for an extended time (or you’re a child whose parents are doing so)… you’re an expatriate. If you’re studying at a foreign school, then I’d feel comfortable calling you an expatriate student. Unless, that is…
…if you’re working abroad and you intend to seek citizenship in your host country… then you’re an immigrant.
Finally, if you’re just wandering the world with no home and no place to which you ever intend to return, you’re an itinerant. You know… voluntarily homeless. ;-)