I've noticed that, when people talk about what can be known about God by the natural light of reason vice faith in revelation, they often use terms like "the Christian God" and "the God of the Bible."
I understand the point -- to emphasize that what we can know with certainty about God by reason falls far short of what we can know with certainty about Him by faith -- but I think it's an unfortunate way of expressing it.
It is, after all, the same God.
I think our habits of speech should reinforce our habits of thought, and "the God [or god] of X" is a Biblical formula for identifying and distinguishing God [or god] from gods. To say that the Christian God cannot be known by reason is, literally, heresy, even though the intended meaning be orthodox.
When talking about our Faith, particularly on subjects like natural theology where we are likely to encounter non-Christians (or, for that matter, Christian fideists), we should be careful not to leave room for error to creep in due to our language. In this case, we should be careful to prevent the inference that the God Who can be known with certainty by the natural light of reason is not the God Who so loved us that He sent us His only Son.