Predestination and free will are concepts important to Christian theology and the study of religion and general. Your question is, basically, is it possible that predestination and free will refer to the same thing? If these two do in fact refer to the same thing, would that mean the argument between different Protestant groups on the issue is not a true argument?
One way to approach your question is to consider the limits of our own knowledge. There is much about human behavior we do not understand. Even looking at our own personal behavior subjectively, we may ask: "why did I do that?" or, "why do I behave like that?" without really knowing why. We may do things that result in harm to ourselves or others, even though we know these behaviors are not best. So, in a sense, the ideas of free will and predestination are both attempts for us to understand how and why we behave the way we do.
Both these ideas do in a sense refer to the same thing: our ignorance; or, our not knowing and not understanding the mechanisms of our own behavior. Thus, both these ideas include an aspect of faith or belief. Neither free will nor predestination are provable hypotheses. They are concepts we use to try to understand our complex lives.
Considering that neither of these concepts are provable, we might conclude that the religious argument about them is not very fruitful. At the same time, we know that the assertion of faith is important to many in terms of their religious identity. For some, defending free will over predetermination (or vice versa) may function as an act of religious piety or even religious duty. Thus, we cannot say these argument are entirely useless, as they serve an important purpose in an individual's religious identity.