What is MOV?
MOV is QuickTime's container - what iPhones and Macs record. The open secret is that MP4 was standardised *from* it, so the two share their internal structure almost exactly, and reading one is reading the other. Writing a true MOV is another matter, which is why it converts from here but not to.
What is MP4?
MP4 is the container video actually travels in - what phones record, what messaging apps accept, what every player since the iPod era opens. It usually carries H.264 video, and its one structural quirk matters to converters: the index of every frame lives in a table that has to be exactly right, or nothing plays.