MP4 vs MOV

MP4 was built on Apple's QuickTime file format, so the two are close relatives. The same video can live in either with no difference in quality.

MOV (QuickTime)MP4
OriginApple, 1991ISO standard (2001), based on QuickTime
Typical codecsH.264, HEVC, ProRes, PCM audioH.264, HEVC, AV1, AAC audio
ProRes / PCMYes, nativelyNo
Windows & AndroidPlays in most apps; some web forms refuse .movPlays everywhere
QualitySame as MP4 for the same codecSame as MOV for the same codec
SizeSame for the same streamsSame for the same streams
Best forApple editing workflows, ProRes intermediatesSharing, uploads, the web

Switching between them

MOV to MP4, and back, is almost always a remux: the H.264 or HEVC stream is copied into the other container without being touched. The catch is HEVC: an iPhone HEVC clip stays HEVC after remuxing, so if a Windows PC or web app still refuses it, re-encode to H.264.

Convert MOV to MP4 MP4 to MOV

Questions

Why do iPhones record MOV instead of MP4?

MOV is Apple's QuickTime format and it supports Apple-specific metadata (Live Photo pairing, some camera data). The video inside is the same HEVC or H.264 that an MP4 would hold.

Can I just rename .mov to .mp4?

Often it works, because both use the same ISO base media structure, but some MOV-only features can confuse players. A proper remux rewrites the header correctly and takes seconds.

Which is better for editing?

For H.264/HEVC, neither. For heavy editing, ProRes in MOV is easier on your computer because each frame is compressed on its own.