My anecdotal experience would seem to indicate that to the adherents of the three major monotheist religions (the majority of the world) the term god refers to the creator of the universe, a perfect, omnipotent, omniscient, omnipresent entity.
Well, sort of. That is how they typically define their god, and they do so to such an extent that their definition has its own entry in the standard dictionary. But that definition is only good for discussing their particular kind of monotheism.
But in a sense, the general term belongs to the entire English language. It has specific meanings whereby we can refer to phrases such as "Thor is the Norse god of thunder", and as English speakers, know what this means and that it is true. This sense of the term doesn't actually depend on whether or not we are Norse pagan--Christians and atheists speak the same language.
Now, when considering theism proper--such as with respect to the question: "Can theists be rational?", it is a more
general sense of the term that is demanded; if, for some reason, Norse pagans could be critical thinkers, then the answer would be yes.
Furthermore, if we explore the major modern Christian viewpoints, you have the concept of the trinity. God the father (the capital G guy), in most concepts, does indeed fit the bill. But what makes him a god (little g, subject to theism proper) is worth exploring. Going further, Jesus is also god, as is the Holy Spirit, though Jesus and the Holy Spirit didn't create the universe. Satan's also supernatural, but isn't considered a god. Also, Moses could turn rods into snakes and split seas in two, but isn't a god.
The consideration with respect to this post is a sort of blend. I'm an English speaker, and being an atheist, I'm not particularly attached to specific definitions of "god". So when I have to refer to the thing people believe exists that makes them theist, I'd like a more general sense of the word--something that makes Jesus, the Holy Spirit, and Thor gods, but not Satan and Moses. Merely being supernatural doesn't do the trick, nor does creating the universe.