Is a sidechain signal always a different signal to the one being compressed?
No. A common but misleading shorthand way of refering to using an external signal for a compressor is to say it’s being ‘sidechained’. The sidechain of a compressor is actually the section of the compressor that detects transients in the signal and adjust the volume of the main signal. It can be either internal, which means the sidechain uses a copy of the main signal to detect, or external, where any signal can be used.
