Is the second set of commandments different from the first? If so, why?

We learn from the Old Testament book of Exodus that, after Moses had been on top of Mount Sinai for 40 days, When the Lord finished speaking to Moses on Mount Sinai, he gave him the two tablets of the Testimony, the tablets of stone inscribed by the finger of God—Exodus 31:18. What God specifically said to Moses is contained in Exodus chapters 20-31. This section of Scripture, of course, includes God’s pronouncement of the Ten Commandments, which is what was specifically inscribed on the tablets of stone. Unfortunately, the nation of Israel, unnerved by Moses’ long absence, committed an incredible sin, supported in their sin by Moses’ brother Aaron: When the people saw that Moses was so long in coming down from the mountain, they gathered around Aaron and said, “Come, make us gods who will go before us. As for this fellow Moses who brought us up out of Egypt, we don’t know what has happened to him.” Aaron answered them, “Take off the gold earrings that your wives, your sons and your daughters are wearing, and bring them to me.” So all the people took off their earrings and brought them to Aaron. He took what they handed him and made it into an idol cast in the shape of a calf, fashioning it with a tool. Then they said, “These are your gods, O Israel, who brought you up out of Egypt.” When Aaron saw this, he built an altar in front of the calf and announced, “Tomorrow there will be a festival to the Lord.” So the next day the people rose early and sacrificed burnt offerings and presented fellowship offerings. Afterward they sat down to eat and drink and got up to indulge in revelry—Exodus 32:1-6. Clued in by God what was going on, Moses (accompanied by his aide, Joshua) returned down the mountain to the camp and witnesses firsthand what they were doing. As the Scriptures say, Moses turned and went down the mountain with the two tablets of the Testimony in his hands. They were inscribed on both sides, front and back. The tablets were the work of God; the writing was the writing of God, engraved on the tablets. When Joshua heard the noise of the people shouting, he said to Moses, “There is the sound of war in the camp.” Moses replied: “It is not the sound of victory, it is not the sound of defeat; it is the sound of singing that I hear.” When Moses approached the camp and saw the calf and the dancing, his anger burned and he threw the tablets out of his hands, breaking them to pieces at the foot of the mountain—Exodus 32:15-19. Of course, there was some serious sin to resolve (not to mention the deaths of 3,000 and the suffering from a plague) but, eventually, Moses (and Israel) did get the tablets back: The Lord said to Moses, “Chisel out two stone tablets like the first ones, and I will write on them the words that were on the first tablets, which you broke. Be read in the morning, and then come up on Mount Sinai. Present yourself to me there on top of the mountain. No one is to come with you or be seen anywhere on the mountain; not even the flocks and herds may graze in front of the mountain.” So Moses chiseled out two stone tablets like the first ones and went up Mount Sinai early in the morning, as the Lord had commanded him; and he carried the two stone tablets in his hands. Then the Lord came down in the cloud and stood there with him and proclaimed his name, the Lord—Exodus 34:1-5. And after another forty days and forty nights on Mount Sinai, the second set of stone tablets returned to the nation of Israel with the Ten Commandments inscribed on them—done, once again, by God: Moses was there with the Lord forty days and forty nights without eating bread or drinking water. And he (God) wrote on the tablets the words of the covenant—the Ten Commandments—Exodus 34:28. As it appears that God Himself actually wrote on both the first and second sets of tablets, it is likely that they were the same.