When one Capitalizes (God) they are referencing "the one and only God."

The Holy Bible says,"I am the Lord, and there is no other; apart from me there is no God." (Isaiah 45:5).

You are right in saying that God is one and there is NO other but him. (Mark 12:32).

And when god is written in lower case (god) they are referencing "the false god."

The Holy Bible says, How long will you love delusions and seek false gods. (Psalm 4:2).

God said,"You shall have NO other gods before Me." (Exodus 20:3).