I just want to point out that it's a pretty big leap to go from "I observed the same frequency response curve with two different inputs" to "there is no audible difference between the two inputs". There are many other measurements you would need to take to prove or disprove the hypothesis, such as signal to noise ratio and dynamic range. And even then you couldn't really prove it definitively due to the complexity of how humans interpret the sound.

When you use Bluetooth, your speaker is functioning as the DAC (digital to analog converter), but when you use the aux, your computer is functioning as the DAC and also amplifying the signal, so it's reasonable to expect them to sound different.