This can be understood from the pasuk, “וּשְׁמַרְתֶּם וַעֲשִׂיתֶם .../You will keep and you will do …” (Devarim 4:6) Chazal tell us that “וּשְׁמַרְתֶּם/You will keep” refers to negative commandments. Negative commandments are generally associated with fear or awe whereas positive commands are associated with love. The feeling of fear or awe which prevents us from transgressing negative commandments corresponds to the concern which keeps us in a state of preparedness for performing mitzvos with love. Through this state of preparedness we merit “וַעֲשִׂיתֶם/and you will do”, referring to the positive commandments. We find this concept in a pasuk in Tehillim as well, “סוּר מֵרָע וַעֲשֵׂה־טוֹב/Turn from evil and do good.” (Tehilim 34:15) Turning from evil prepares us to do good.
Moshe Rabbeinu certainly did not change what God said. Chazal tell us that God said, and we heard, both זָכוֹר/Remember and שָׁמוֹר/Keep simultaneously. The mitzvah of keeping Shabbos actually comprises both a positive and negative commandment. זָכוֹר/Remember, refers to observing the positive commandment of Shabbos. שָׁמוֹר/Keep, refers to the negative commandment of Shabbos.
On a deeper level זָכוֹר/Remember on its highest level is not really remembering at all. Rather it is a connection to something at such a deep level that it becomes a part of us to the extent that there is no possibility of forgetting. This is a very high level that not everyone merits reaching. However, Chazal are teaching us that a person who is careful about שָׁמוֹר/Keep – a person who keeps himself in a constant state of preparedness, whose primary concern is to do mitzvos – God’s will – is included in זָכוֹר/Remember on its highest level as well. That person will merit achieving God’s will.