I think what separates a Real Traveler from a mere tourist is simply the enjoyment of objectively bad experiences so long as they are novel, at least in retrospect. For example, I got locked out of my abode once while in Chicago, and had to spend the night on the streets in the cold getting harangued by the local cretins. It was awful, but it's a cherished travel memory of mine because I learned quite a few things from the experience. I've noticed the people who I travel with that don't seem to enjoy traveling much are those who needs things to go according to plan, who are disappointed when expectations are not met, who need some minimum sense of luxury to enjoy leaving their home.
So a Real Traveler is not really defined by how many countries they've been too, or their passport, or their budget, but really just by their lust for going somewhere new just for the hell of it.