Of course you need. As Apple Music files are protected which can't be used outside Apple Music app, you need to convert Apple Music to MP3 before using them on other devices. After then, you can use the files directly.
All songs from Apple Music exist in the format of AAC files. As they’re protected by a special kind of DRM, you are not able to play them on any device without the Apple Music app. so you may need to convert M4P to MP3 then could load the music to app.
There are so many professional Apple Music Converter tools that allow you to download and convert Apple Music to MP3. You just need to choose your favorite one to do that. By the way, Apple Music files are protected by DRM, you'd better use a tool that can remove protection.
The one I'm using is called AudFree Audio Converter, which can do them both at a 30X faster speed. With the help of it, you can easily DJ with Apple Music on your Samsung devices.