In 5:12, as Moshe is transmitting the second set of the 10 Commandments, he says, "שמור את יום השבת" - Guard the day of Shabbos to keep it holy.
Rashi brings the famous question that in the first set of Commandments the word used for keeping Shabbos is 'Zachor' - 'remember', while here in the second set it uses the term 'Shamor' - 'Guard'. Why the change? and Rashi explains that both words were said at the exact same moment, and they were divided up between the two sets of commandments for us.
Yet the question still remains why 'Zachor' was chosen to be immortalized in the first set of commandments and 'Shamor' in the second set? Why not write both both times, or write the opposite order? Why write first 'zachor' and then 'shamor'? If both were said, then both should be written in the surviving luchos!
I do not have an answer to explain why it chose to write 'zachor' and one and 'shamor' in the other. But perhaps we can understand that once it did shoose to break it up and seperate the two words into the two tablets, why it chose to write 'zachor' first and 'shamor' second.
I would suggest that this order points us to an understanding of our history and of our approach to Judaism and mitzvos.
'Zachor' - remembering, is a passive approach to Judaism and mitzvos.
'Shamor' - guarding, is a more active, and proactive approach to Judaism and mitzvos.
Being passive has a danger to it; the danger that you will miss something, you will not perceive a threat to your lifestyle, you will not react to a threat, etc.You might not recognize the time has come to act.
At first, the passive approach was dominant. The Jews were mostly living a life, in the early desert years, of everything being done for them. Moshe broke the luchos because he saw where their passivity had brought them.
The second luchos say 'shamor' becausenow God demands a much more proactive approach to Judaism and to mitzvos. Don't just remember shabbos, but guard it.
'Shamor' is written in the surviving set of luchos, because in order to survive, as a people, as a nation, as Jews, we have to be proactive in our service of God.