While I presume you are correct, and that the commandment listed 1st here is meant to incorporate the section about idols, the site implies that the text of the commandment as taught would not include the term about idols.
- I am the LORD your God. You shall worship the Lord your God and Him only shall you serve.
- You shall not take the name of the Lord your God in vain.
- Remember to keep holy the Sabbath day.
- Honor your father and your mother.
- You shall not kill.
- You shall not commit adultery.
- You shall not steal.
- You shall not bear false witness against your neighbor.
- You shall not covet your neighbor's wife.
- You shall not covet your neighbor's goods.
Both the Exodus and Deuteronomy passages include the text about idols, and it is true that most christian faiths break out the idol text as the 2nd commandment. In fact, I was unaware that the Catholic Church did it differently. Also, it appears the Jewish faith for which the 10 commandements were originally given counts the Idol text as the 2nd commandment, but only because they cound "I am the lord your God" as a commandment, and then lump "no other gods" and "idols" together.
I know that the PCA church, at least in some of their specific churches, put a good bit of emphasis on idol worship -- my particular church for example will not have pictures of Jesus, or endorse films depicting him (can't say I agree with that).
So, in light of my meager investigation, could you clarify your point about the difference between the 10 commandments and how it doesn't actually change anything?
We always learned it as part of “You shall not have any gods before me. You shall make no graven images.”