Yes it only considers the combined total mix, not each individual source. All it can do is measure the soundwave that actually reaches your ear, using a built in microphone.

Think of being in a pool. You've got 4 different people swimming, splashing, diving in - making different sizes and types of waves at different locations. But that doesn't really matter - you're at one end of the pool with a little float that bobs up and down and traces the net combined total of all these waves as their combined peaks and troughs reach you.

That little float is like the microphone in noise-cancelling headphones. The microphone measures the total net combined sound wave peaks and troughs reaching your ear, and then the headphones play an "opposite sound" that has peaks where the room noise has throughs and troughs where the room noise has peaks. The peaks and troughs cancel, and the room noise is imperfectly but substantially eliminated.

And yes it's an engineering marvel that this measurement and active response can happen at the speed of sound in an ear-sized device.

think of waves in a bathtub or pool, or even an ocean. the waves are highly complex, and you may not be able to cancel them all perfectly, but if you can just knock down the peaks and troughs, you'll make things much smoother.

Throw in some white noise and you can drown out the rest.

It doesn't detect them as multiple frequencies until later, it just samples the incoming sounds and creates a digital version of the analog measurements. from the mic.

There's a thing called 'digital signal processing' which then can then analyze the digital signal and break it up into it's composite frequencies/magnitudes, average out the noise. The way the processing is handled will determine the quality of the end result.

Some cool things to learn about would in Nyquist Theorem, Fast Fourier Analysis, and Digital Signal Processing (FFT is part of this but deserves it's own mention).