Not the same
Windows Live Moviemaker is the succssor to the old Windows Moviemaker. They are not the same program. The successor is easier and more powerful and can handles more codecs.
And, renaming the file extension does not alter any properties of the video file, so it is not like changing unleaded gasoline to leaded. There is no conversion; thus, no loss of quality.
WLM is a basic program, like Media Impression, but it is free and I think somewhat more powerful, and certainly less crash-prone, than Media Impression. Just weird you have to change the extension from .mov to .mp4 because the video is exactly the same.
Btw, the same thing is true for Sony Vegas Pro. It actually can crash if you try importing a .mov file. Change the extension to .mp4 (not a conversion), and no problem.