The Second Commandment – Is it Different from the First?

It occurred to me that the 1^st and 2^nd of the Ten Commandments are redundant if you do not have the proper understanding of what each one means. Read them and think about it:

Exodus 20:3 – You shall have no other gods before Me.

Exodus 20:4 – You shall not make for yourself a carved image – any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth; you shall not bow down to them nor serve them…

Depending on what you believe about how these two commandments are interpreted, they may appear redundant. The 1^st commandment says that you should have no other gods besides the true God. Some mistakenly assume that the 2^nd commandment is exclusively talking about idols. If so, then it is redundant, since an idol is a false god, and is therefore prohibited by the 1^st commandment. This begs the question: is the 2^nd commandment simply an elaboration on the 1^st, or is it addressing a separate issue?