Why the difference in audio volume via bluetooth?
Every output device has a maximum volume level in its settings. This is different than the current listening volume of the main volume. 

For instance,  I have internal speakers, external speakers, alerts, midi Dj'ing equipment and bluetooth PA system speakers.

If I go to the sound preferences, there are different default volumes for each device. No matter the main volume those will override current main volume on plug in , activation or connection of a different device.

Individually they all have their own settings and ultimately they can be found in the sound preferences.

Then as some mentioned, the device you are connecting to, can also have its own defaults that override your connecting device.