Can humans distinguish light having the same color but different spectrum?
If by "same color in RGB space" you mean "activates human cones the same way" then the answer is no: color perception is based on the ratio that different cones are activated at. There is no difference between a spectrum that has a smooth distribution across wavelengths or one that is properly calibrated into three or more specific peaks.

This concept is why RGB monitors and TV screens work to produce just about every color (though there are of course limits to the spectrum that a RGB monitor can produce, but that is a technological limitation).