MOV and MP4 are closely related formats. Both are based on Apple's QuickTime container specification, and both commonly carry H.264 or H.265 video. The main difference is that MOV is Apple's preferred container while MP4 is the universal standard. Most of the time, converting between them is nearly instant because you don't need to re-encode the video.
The fastest method is remuxing — copying the video and audio streams into a new container without re-encoding. This is instant (a few seconds for a large file) and completely lossless. FFmpeg does this with: `ffmpeg -i input.mov -c copy output.mp4`. The video data isn't touched; it's just repackaged.
For a simpler approach, fwip and other browser-based tools handle MOV to MP4 conversion directly. Drop the file, get an MP4 back. If the MOV contains H.264 or H.265 video, the conversion is a quick remux. If it contains an older codec (like Apple ProRes), the tool will re-encode to H.264.
On Mac, you can also use iMovie (free) or QuickTime Player. In QuickTime, open the MOV file and choose File → Export As → 1080p (or other resolution). This re-encodes the video, which is slower but ensures maximum compatibility.
One note for iPhone videos: iOS records in MOV by default, but you can change this in Settings → Camera → Formats → Most Compatible, which saves as MP4/H.264 going forward.