The answer is simple, it depends entirely on the file format used.
- Does the specification of the format allows for tagging?
- If so, is there a standard?
MP3 can be tagged using ID3 standard.
FLAC can be tagged using OGG/Vorbis comments
WAV is something in between, it can be tagged but there is no standard.
That is why tags in WAV in general don’t carry over to another media player.
A simple test:
Tag a file
Move it to another computer
Check if and if so what tags are carried over.