Yes. The mp3 tags are stored within the mp3 file itself. Some players can extend the tags, or store their meta data elsewhere (e.g. in their own local database), so if you want the meta data to be portable you need to use the widely used id3 standard.
I've personally never used the mp3tag program, and use the second one I linked to you. It can be a bit complicated to learn but it's fairly simple once you get the basics down.