None of the ehm “official” releases of the Harmy editions have menus.
MKV is just a container, it “contains” the video stream, multiple audio streams and I’m not sure if the subtitle streams were muxed into the mkv file or if they were distributed separately. So you simply play the mkv file in your favorite player, choose your audio track (and your subtitle track) and you watch the movie directly, there are no menus. So you can play it on your computer, or directly on your TV from some USB stick if your TV supports it or you can play it from your BluRay player - again, if your player supports the mkv format (check the manuals or online reviews before burning it to a BD).
AVCHD is basically the same format as BluRay, but it’s smaller. In other words you can burn it on a dual layer DVD and put it to your BluRay player and the player will play it automatically - again, if it support AVCHD discs. But even the AVCHD doesn’t have a menu.
So the basic difference - mkv is one file containing video and audio streams, the AVCHD is either an iso image or a folder structure full of m2ts (and other) files. Most people who are on Windows seem to use ImgBurn or Nero or something like that.
And “official” Bluray of all 3 movies was planned at one point, and it should have nice menues, not sure if it was cancelled or if it’s still being worked on. But if you DON’T require a menu and you want a BluRay, you can use the free TSMuxer to create a BD structure from the mkv file for you.