The Ten
Commandments

Exodus 20:1 And God spoke all these words:
 

NO FALSE GODS

Exodus 20:2-3  [2] I am the LORD your God, who brought you out of Egypt, out of the land of slavery. [3] You shall have no other gods before me.

NO IDOLS

Exodus 20:4 You shall not make for yourself an idol in the form of anything in heaven above or on the earth beneath or in the waters below.

DON'T MISUSE THE LORD'S NAME

Exodus 20:7 You shall not misuse the name of the LORD your God, for the LORD will not hold anyone guiltless who misuses his name.

KEEP THE SABBATH

Exodus 20:8 Remember the Sabbath day by keeping it holy.

HONOR PARENTS

Exodus 20:12 Honor your father and your mother, so that you may live long in the land the LORD your God is giving you.

NO MURDER

Exodus 20:13 You shall not murder.

NO ADULTERY

Exodus 20:14 You shall not commit adultery.

NO THEFT

Exodus 20:15 You shall not steal.

NO PERJURY

Exodus 20:16 You shall not give false testimony against your neighbor.

DON'T COVET

Exodus 20:17 You shall not covet your neighbor's house. You shall not covet your neighbor's wife, or his manservant or maidservant, his ox or donkey, or anything that belongs to your neighbor.

"I remember the Ten Commandments differently."

Due to the large number of statues of various saints in Catholic churches, the Roman Catholic Church combines Exodus 20:2-6 as a single commandment and breaks Exodus 20:17 into a "Don't covet your neighbor's wife" and a "Don't covet your neighbor's goods" command, to de-emphasize the "don't make an image" aspect of the second commandment.

A simplistic response to their approach is "No idols is in a separate verse."  However, verse numbering was added way after the Bible was written.

If you study the Bible enough, e.g., Isaiah and Ezekiel, it becomes pretty obvious that God distinguishes between idols and false gods, although there is some overlap.  Generally, a false god is either a figment of the person's imagination or a demon spirit pretending to be a god.  On the other hand, an idol is a thing built by man or occuring naturally, e.g., a statue, the Sun, or the Moon.
 

Also see What God Requires of Us.