Sometimes in the Torah, a single event is described more than once. For example, after the event occurs (i.e. Avraham's servant meeting Rivkah at the well, or Pharaoh dreaming), a character describes it to other characters. Yet the Torah's text in the two cases differs somewhat, even though the exact same events are being recorded. When this occurs, we must ask ourselves why. Are the differences just matters of style? Or are they substantive, and if so why do they exist? The answers to these questions will vary from case to case.
One interesting example appears in the Ten Plagues. Regarding the plague of hail, God commands Moshe to speak a certain speech to Pharaoh, but it is not recorded that Moshe then spoke to Pharaoh. Regarding the plague of locusts, God commands Moshe to go to Pharaoh (without mentioning locusts), after which Moshe tells Pharaoh about the coming plague of locusts. Ramban (on Shemot 9:19 and 10:2) says the differences here are just matters of style. Moshe really did give the hail speech to Pharaoh, and God did tell Moshe about the locusts ahead of time. But the Torah did not mention these events, as they are too repetitive and can be inferred from context.
However, in another case a few chapters away, I think the understanding is quite different. In this case, God twice tells Moshe to instruct the people about something. But then Moshe seemingly instructs the people something quite different from what God instructed him.
In Shemot 12, known as "HaChodesh", God commands Moshe regarding the Pesach sacrifice, the upcoming 10th plague, and the "Hag Hamatzot" holiday which will commemorate this event for the generations. Moshe calls together the elders of Israel, and tells them about the Pesach sacrifice and the 10th plague - but does not mention the holiday.
In Shemot 13:1-2, just after leaving Egypt, God issues a very concise command: to consecrate all firstborns among Israel. Moshe, then, gives a long two-paragraph speech to Israel. The first paragraph describes the seven-day holiday commemorating the Exodus, while the second paragraph mentions consecration of firstborns. Both paragraphs mention telling your son about the Exodus, and having a "sign on your hand, and a memory/phylactery between your eyes" to commemorate the Exodus.
To summarize: In Shemot 12, God talked about three subjects (sacrifice, plague, and holiday) while Moshe talked about two (sacrifice and plague). In Shemot 13, God talked about one subject (consecration) while Moshe talked about two (holiday and consecration).
We notice that the one topic Moshe missed in Shemot 12 is the topic he adds in Shemot 13! Therefore, it seems to me that Moshe delayed telling the people about the holiday until after they had left Egypt.
Here is my hypothesis: God mentioned as many commandments as possible before the Exodus (the sacrifice, plague, and holiday). But God could not mention consecration of firstborns beforehand, because that is one side in a transaction, and God could not ask Israel to "pay up" before doing HIS side of the transaction. Whereas Moshe told the people only what was relevant to them at each time: they had to know about the sacrifice and plague ahead of time, but the holiday was not relevant until after leaving Egypt, so Moshe waited to tell the people until later. When he did tell them, he combined this command with another command he had received in the meantime: consecration of firstborns.
In summary: We have identified a total of four topics in God's commands, and the same four topics in Moshe's commands, and explained why each topic appears when it does. That said, each of the four topics has a somewhat different text in God's vs Moses' telling. To reconcile the different texts within a single topic, I would probably go with the Ramban's approach as described above. This approach seems best for when text is "missing" from one of the two accounts in the Torah. But when text is "shifted in position" rather than "missing", we should assume it was said where it appears, and look for an explanation of why this occurred.