Re-eh vs. Mishpatim

Last weeks Parsha uses the word "nivalah," which I understand to mean an otherwise kosher animal that dies on its own, and says that "you shall not eat it, but you may give it to the stranger in your cities . . . or you may sell it to a foreigner." In contrast, Parsha Mispatim uses the word "treifa," which I understand to mean an otherwise kosher animal that dies by being torn by beasts, and says that "...and flesh torn in the field you shall not eat; you shall throw it to the dogs." The Ibn Ezra says with respect to treifa is that it is only fit for the dogs, and Rashi says that treifa is the dogs reward for not barking when the Israelites left Egypt. It seems then that treifa must be given to the dogs, and not sold or given to gentiles. Notwithstanding the modern use of "treif" as anything not kosher: So why then do the majority of the commentaries seemingly claim that treifa and nivalah mean the same thing? In my humble opinion, this does not appear to be correct; otherwise the Chumash would have used the same word in both instances. Any thoughts?

You are correct, that neveila and treifa are different, but the truth is, all commentaries agree as well (as is clear from their roots), just that some of their halachot are similar, while others are different, e.g. that the treifa is best to give to dogs, and neveila can be sold l'chatchila to gentiles.