What you are hearing is not a plastic plectrum striking a steel string but the soundwaves travelling through the air that this action produces. Actually, you are mostly hearing the resonance of the wooden body in the case of an acoustic guitar.
Speaker cones of different materials can produce reasonable facsimiles of those soundwaves and also of many other instruments made of different materials all at once. Your speakers don’t produce an exact copy of the soundwave but close enough to satisfy most people.
The cone doesn’t have to be made of the same material, just be able to make similar waves in the air.
This is a very simple explanation, and probably not what you wanted, but I’m sure someone else will do better.