There is no reason for introducing two different terms. Apparently, somebody introduced one term, and somebody else introduced a different term, either because he didn't like the first guy's term, or he hadn't heard of it. Or maybe it was the same guy and he changed his mind, or forgot what he called it before. How would I know, I'm not a historian (nor a mathematician).
The point is, in mathematics there is no official body with the power to decide what the terminology should be. This is different from other sciences, such as astronomy, where some organization claims the power to decide what's a planet. In mathematics, each writer goes his own way, and anarchy prevails. (If you think "model" vs. "structure" is bad, look at the terminology of graph theory.) Eventually, after a few centuries, a consensus is reached. Obviously, model theory (and graph theory) are too young to have reached that point.