Aux or bluetooth

What is the difference between tethering by Bluetooth or using a auxiliary cord to plug in from your smartphone to another radio speaker which will allow you to hear podcast or radio station from the internet.
Does using a Aux cord use data and does a wireless carrier charge extra for this like if you were using your phone as a mobile hotspot?
 
If the file being played is on the phone its not using mobile data, if it is streaming from the internet it does.
Doesn't matter whether the connection from phone to speaker is wired or bluetooth, those aren't costing anything or change how the data is arriving at your phone.