In my mind I was thinking of the Christians idea of God. So in the next line I was about to think to myself “Is God the most beloved to them” Here by the word God I meant Their God in which they believe in But after I said “Is God” I thought to myself that I didn’t mention their God Even though I meant it from my heart But if I said this line Without mentioning Specifically that I meant their God But meant it from my heart Is it shirk? (Again this whole thing is inside my head)
It is not shirk. It all depends on your intentions. If you intended on thinking about their God but failed to mention it out loud your intentions will be judged by Allah, for He will know what you meant while saying that.
Further justified by a Hadith which was stated by our Holy Prophet(PBUH) after their Hijrat(Pilgrimage) from Makkah to Madina; "Deeds are according to the intentions" (translated into Urdu "Amaal ka daromadar niyat par hai"). This shows that even though your intentions were not related reward-gaining, you also did not mean any offence to our faith, therefore, I am sure you did not commit shirk.
Other than this, Christians do believe in Allah, even though they do not name Him as that, but they further on believe in Jesus (Prophet Esa AS) as God's son. So I am guessing that you might be considering Jesus when you state God in your query.