What is the difference between Apple Music vs Apple Match

In a nutshell - Apple Music for a fixed price lets you access 30 million + songs.

Apple Match lets you access your own music from multiple devices.

Per Apple, the two services are complimentary

See

http://www.apple.com/music/

See

http://www.apple.com/itunes/itunes-match/

see

https://support.apple.com/en-us/HT204146

You may find this page helpful in explaining what these services do: http://wilmut.uk/applemusic