Are you an adherent of Amarmotamonaxism?
The thought occurs that I am not really a theist.
Oh, that's where I'd be placed if anyone wanted to categorize people as either atheists or theists. But that's a silly way to categorize people. It's like categorizing mammals as either groundhogs or non-groundhogs.
"Non-groundhog" isn't a species of mammal, or even a particularly useful grouping of mammals. Groundhogs may not much care about the specific differences between non-groundhogs, but that's no reason for non-groundhogs to follow suit.
And in fact, we (if I may speak for us) don't. We think of ourselves, we understand ourselves, we live as humans, not as non-groundhogs.
Similarly, we Christians don't (and if we do, I suggest we shouldn't) think of or understand ourselves as theists, we think of and understand ourselves -- perhaps, on occasion, we live -- as Christians. "Christian" is not a sub-category of "theist" in any sense meaningful to the Christian. Faith in Jesus Christ as the incarnate Son Who died for our redemption that we might live forever as children of His Father is not a specific refinement of a general belief in the existence of one or more gods. Or rather, it's a refinement as meaningful to the Christian as the refinement of "non-groundhog" to "human" is to the human.
The above may bring to mind the folktale "The Ugly Groundhog," in which the protagonist comes to realize that he is not a groundhog some time before he finds out he is a human. For him, for a time, "non-groundhog" was a meaningful category.
Similarly, one might point out that there are those whose religious opinions genuinely are no more specific than "I believe in the existence of God." Mortimer Adler held that opinion for years -- though even then, he didn't say he was an undifferentiated "theist." He called himself (with, I assume, a bit of a grin) a pagan.
People may have bare-bones, undeveloped, or inchoate religious opinions, but they don't have generic opinions. That's the difference between the Ugly Groundhog and the non-atheist. No one is a "theist" in only a generic sense, even if there is no specific name for their specific religious opinions.