ANSWER

רש"י is teaching us that משה wrote these two things differently. The first part, the “storyline” from בראשית until מתן תורה, which had already happened at that time, he wrote in the exact same words as the __________ of the תורה that we have today. However, the second part that he wrote were the ________ that we were commanded in מרה. These would only be written in later פרשיות of the תורה. So, he wrote them as instructions that we must follow, but not in the same words in which they would be written in the תורה later. This is why – after explaining that משה wrote “from בראשית until מתן תורה” – רש"י once again writes the word וכתב, to teach us that he wrote these מצוות in a different manner.