Electronic – Understanding the circuit diagrams for white noise generators

Why are Op Amps more noisy than other types of amplifiers (BJT and MOSFET, for example)?

I doubt this is true, especially if you consider the noise factor for the same circuit gain (but another answer might give more concrete information).

So, in short, why do OP Amps have electrical noise issues (if at all), and what is the source?

TI has a couple of good app notes on this:

Chapter 10 of Op-amps for Everyone

Noise Analysis for High-speed Op-amps

In short, the feedback resistors and the op-amp's input stage transistors both contribute to noise.

Perhaps Op Amps lack sufficient filtering capabilities that are inherent to BJT and MOSFET design?

Op-amp circuits can be filtered to whatever bandwidth you like. It only requires adding an extra capacitor or two to the op-amp circuit, or for higher-order filtering adding an additional filter stage after the high-gain stage. Which would be equally required for a discrete circuit.

This is a common problem in audio amplifier connections especially where there is digital noise and switching regulators. There is no ideal way around this problem without using differential inputs.

Why do differential inputs work - the signal return back to the box on the left won't carry any power supply currents because it feeds a high input impedance differential amplifier (or a transformer). Obviously you have to wire it correctly.

Without a differential input (silicon or transformer) it's difficult to find a signal return path that won't pass digital currents.

This problem has nothing to do with dodgy earths in your home or needing to put a decoupling capacitor somewhere.