is titillating the inner recesses of my brain again.
To me, this question appears to answer itself. There is only one God. Therefore, two people who worship Him, are for that reason worshipping the same God. The answer could be otherwise only if there were more than one God.
Okay, I know that answer is simplistic. It depends, essentially, on what is meant by God. I would define the term primarily in terms of aseity
, as our tradition has always done: 'that which nothing greater can be conceived' (Anselm) or 'that whose existence constitutes its essence' (Aquinas). Of course, one does not need to understand, or even to be explicitly aware of, such high-blown technical concepts in order to worship God. But one must at least grasp them in a very implicit, interior manner - e.g., one must know that the Being one is worshipping is not of this world, or at least, is not identifiable with anything in it.
One cannot, then, define God in terms of any of His dealings with creation. Msgr. Sokolowski has the best presentation of this in his The God of Faith and Reason
. Aquinas, however, formulated it most definitively. God has no inherent 'relation' to creation at all, since He is utterly independent of it, and it has no existence apart from Him. Any 'relation' He may have (and this He certainly does!) is completely gratuitious, arising purely from an act of His will which might not have been. This means that God is defined neither by creation nor by 'recreation,' i.e. by the Incarnation of His Son to redeem the world. To make either creation or redemption constitutive of the divine essence is to make that act obligatory upon God, and hence to deny its gratuity.
"Jesus Christ is constitutive of God."
Hmm. I think, again, it depends what you mean by 'constitutive.' If it simply means that Jesus Christ is
God, that God is fully manifested in Jesus in a definitive and unsurpassable manner, then, of course, it is true. But this is not normally what we mean by 'constitutive.' In the normal meaning
of that word, this statement would imply that the divine essence somehow requires
the manifestation of Jesus Christ, in order to be true to itself. And that is simply not true. The statement seems to confuse relation
, in technical language. The divine Son, certainly, is constitutive of God (though not uniquely so), but the Incarnation of this Son in human flesh is not constitutive in this way. Temporal missions of the eternal persons, by definition, are not constitutive of the divine essence.