Do we use the phrase "The Ten Commandments" incorrectly?

It's not uncommon to see people claim this.  I myself had been under similar misconceptions in the past, and had to edit some mistakes out of the post I made earlier today.

Now it's true the narrative presented in the 1956 film The Ten Commandments is garbled.  I mean it arguably undermined the moral of the narrative that they change it so the people hadn't received the Commandments yet when they engaged in the Golden Calf orgy.  DeMille kind of anticipated the Godfather Baptism montage by having them break the Commandments as God writes them.

It is true that they are not being written in Stone when God first gave them in Exodus 20, there they are spoken by Yahuah to the People directly, without even using Moses as a middle man.

It is true that The Bible does not use the exact three word phrase "The Ten Commandments" in Exodus 20, or Deuteronomy 5 where they are repeated.

Exodus 34:28 says of Moses "And he wrote upon the tables the words of the covenant, the ten commandments.".  The context of this Chapter, is kinda unclear about exactly what that means.  It may be, given the issues of translating, that there should be an "and" between "words of the Covenant" and "The Ten Commandments".  I say this based on the fact that the "words of the Covenant' arguably refers to Exodus 20:22-23:33, and the Covenant is then ratified in chapter 24.

At any-rate Exodus 34:28 is about the second set of Stone Tablets, the first set are mentioned in the last verse of Exodus 31, verse 18.  It could be on the original Tablets were only written the information relied in 25:1-31:17.  Israel's breaking of the Covenant with the Golden Calf as these were written, changed things.  Originally the contents of Exodus 20:22-23:33 were written on a scroll as Exodus 24 records.  But that is unclear.  It could have been all three sets of instructions. 

However the people claiming that phrase refers to a mostly completely different set of rules, are ignoring that the phrase appears twice more in Deuteronomy, in 4:13 and 10:4.  Deuteronomy 10:4 defined what that phrase refers to more clearly then any other verse.

"And he wrote on the tables, according to the first writing, the ten commandments, which Yahuah spake unto you in the mount out of the midst of the fire in the day of the assembly: and Yahuah gave them unto me."

That clearly describes the commands given in Exodus 20, Moses is also repeating the wording of how he described that event in Deuteronomy 5:4.

Now one article you'll find online (and I agree with their political point about it violating the Establishment Clause to put the Commandments on Government buildings), gives a list of ten different commands, well at least three overlap, saying that's what Exodus 34:28 called 'The Ten Commandments".  This list is arbitrarily taking 10 of the commands given earlier in Exodus 34, as a warning not to make a covenant with the Canaanites, and they aren't even consecutive.  They are, first is verse 14 worded incorrectly, 17, 18, 21, 22, 23, 25 is split into two commands, and then so is 26.  Just reading chapter 34 you would not see that as listing of ten commands.

Perhaps they would simply argue Deuteronomy is contradicting Exodus.  But even on it's own, you have to draw some flimsily conclusions to think Exodus is calling that list of more then 10 instructions the Ten Commandments.

Exodus 34 defines what was written on the second Tablets as the same thing written on the first.