When streaming, you can listen to music directly without downloading them before. This is not possible when your mobile is not connected to the Internet. You need a good Internet connection. If not you risk that the songs you listen to might be interrupted from time to time.
When listining offline, you can listen to music without being connected to the Internet. You don't consume your data flat. However, you need to download the music first to your mobile phone by activating the option "Offline access" in your app.