Why are the ten commandments in Exodus 34 different?

Question

The first stone tablets with the ten commandments were smashed by Moses, so God created a second set of stone tablets that were supposed to contain the same commandments as the smashed tablets. But the actual text of the second set of commandments that follows in Exodus 34 is different from the original commandments.

Why is this second set different from the original ten commandments?

Exodus 34 (KJ21)
   And the LORD said unto Moses, "Hew thee two tablets of stone like unto the first, and I will write upon these tablets the words that were in the first tablets which thou brokest.

[...]

   
 ¹¹Observe thou that which I command thee this day. Behold, I drive out before thee the Amorite and the Canaanite, and the Hittite and the Perizzite, and the Hivite and the Jebusite.
   
 ¹²Take heed to thyself, lest thou make a covenant with the inhabitants of the land whither thou goest, lest it be for a snare in the midst of thee.
   
 ¹³But ye shall destroy their altars, break their images, and cut down their Asherah poles.
   
 ¹⁴For thou shalt worship no other god; for the LORD, whose name is Jealous, is a jealous God,
   
 ¹⁵lest thou make a covenant with the inhabitants of the land and they go a whoring after their gods, and do sacrifice unto their gods, and one call thee and thou eat of his sacrifice,
   
 ¹⁶and thou take their daughters unto thy sons, and their daughters go a whoring after their gods, and make thy sons go a whoring after their gods.
   
 ¹⁷"Thou shalt make thee no molten gods.
   
 ¹⁸"The Feast of Unleavened Bread shalt thou keep. Seven days thou shalt eat unleavened bread, as I commanded thee, in the time of the month of Abib; for in the month of Abib thou camest out from Egypt.
   
 ¹⁹"All that openeth the womb is Mine, and every firstling among thy cattle, whether ox or sheep, that is male.
   
 ²⁰But the firstling of an ass thou shalt redeem with a lamb; and if thou redeem him not, then shalt thou break his neck. All the firstborn of thy sons thou shalt redeem. And none shall appear before Me empty.
   
 ²¹"Six days thou shalt work, but on the seventh day thou shalt rest; in plowing time and in harvest thou shalt rest.
   
 ²²And thou shalt observe the Feast of Weeks of the firstfruits of wheat harvest, and the Feast of Ingathering at the year's end.
   
 ²³Thrice in the year shall all your menchildren appear before the Lord GOD, the God of Israel.
   
 ²⁴For I will cast out the nations before thee and enlarge thy borders; neither shall any man desire thy land when thou shalt go up to appear before the LORD thy God thrice in the year.
   
 ²⁵"Thou shalt not offer the blood of My sacrifice with leaven, neither shall the sacrifice of the Feast of the Passover be left until the morning.
   
 ²⁶The first of the firstfruits of thy land thou shalt bring unto the house of the LORD thy God. Thou shalt not boil a kid in his mother's milk."
   
 ²⁷And the LORD said unto Moses, "Write thou these words, for according to the tenor of these words I have made a covenant with thee and with Israel."
   
 ²⁸And he was there with the LORD forty days and forty nights; he neither ate bread nor drank water. And He wrote upon the tablets the words of the covenant, the Ten Commandments.

Answer 1

Those aren't the words written on the second stone tablets.

The original tablets were written by the Lord:

Exodus 24:12 (ESV)
The LORD said to Moses, "Come up to me on the mountain and wait there, that I may give you the tablets of stone, with the law and the commandment, which I have written for their instruction."

Compare to the passage referred to in the question. The Lord says he will write the tablets, but the commandments cited in the question are left for Moses to write:

Exodus 34:1 (ESV) ^{[emphases mine]}
The LORD said to Moses, "Cut for yourself two tablets of stone like the first, and I will write on the tablets the words that were on the first tablets, which you broke.

Exodus 34:27 (ESV) ^{[emphases mine]}
And the LORD said to Moses, "Write these words, for in accordance with these words I have made a covenant with you and with Israel."

After the Lord gave the original ten commandments (Exodus 20), he also gave other commandments (Exodus 20:23-23:33). A similar thing happened here: there were other things that the Lord said to Moses, besides just writing the new tablets.

The quite logical explanation is, then, that the Lord wrote the new tablets and gave them to Moses. Then the Lord spoke other words and told Moses to write them down. The content of the tablets is not recorded in Exodus for a second time, since the content was the same as originally.

Answer 2

The Exodus 34 commandments are sometimes called the Ritual Decalogue, as opposed to the Ethical Decalogue that most people are familiar with from Exodus 20. The Wikipedia page above lists the various theories of why these two sets of commandments are different.

One theory points out that this second set of commandments follows the incident of the golden calf, and so is an addition to and expansion of the first with a greater focus on worshiping God and avoiding idolatry.