Convert from MOV to MP4 Container format

I don't want to touch the actual quality of the video I want the conversion to be as fast as possible.

Use FFmpeg with -c copy to just copy the contained data (video, audio, subtitles).

ffmpeg -i file.mov -c copy out.mp4
ffmpeg -i file.mov -c copy out.mkv

If there are more than one video / audio / subtitle stream, and you want to copy all, use:

ffmpeg -i file.mov -c copy -map 0 out.mp4

The MOV container is compatible to MP4 and it supports all video and audio bitstreams that MKV supports as well. You can simply copy the video and audio data to the output container without touching the raw bit streams.

This will be the fastest conversion, since it actually doesn't encode anything—and you'll retain the quality of the original.

Download and install FFmpeg:

• On macOS/Linux through Homebrew with brew install ffmpeg or a static build from the download page
• On Linux via static build from https://ffmpeg.org/download.html, or also via Homebrew

VLC allows you to switch containers.

Select Media->Convert/Save, select files, Convert->Save, click "Create New Profile" icon, change container, mark keep original video and audio tracks.

You can re-pack MOV to MKV easily with mkvtoolnix. It has both command-line and GUI tools for Windows and Linux:

mkvmerge -o output.mkv input.mov

It just changes the container, without recoding anything. You said "more respecatble format like mp4, so I suppose MKV would work for you.