Not sure how I can explain it better
Here's how:
I see three wires coming out of the wall in your original photo. Label them A, B and C in whatever order you please.
While the doorbell button(s) not pressed, what is the voltage when you probe:
A and B:
A and C:
B and C:
While the first doorbell button pressed, what is the voltage when you probe:
A and B:
A and C:
B and C:
If you have another doorbell button, for example a back door, while the second doorbell button pressed, what is the voltage when you probe:
A and B:
A and C:
B and C:
Was either doorbell button known to be illuminated when it worked?