Is there any difference in the way we perceive two objects, one that reflects white light and another that emits white light?
As you've written the question, with exactly the same light reaching the eye, then they'll be perceived the same.
But perception is complicated. It depends on the light reaching the eye from a point, but also lots of other things.
To see that:
- Look at a projection screen with the projector off. What color is it? Usually white or light gray
- Now have the projector project black text on a white background. The letters are black, right?
But those letters in the second step are sending to your eye exactly the same light as the screen was in the first step: The projector has made other parts of the screen brighter, and that makes your brain consider as black something that used to be considered as white.
This is why "emitting light" is often considered to look differently from "reflecting light". The emitting case is usually brighter (because it's emitting and often reflecting some light) than the reflecting case, and that can make it look very different.
Imagine a source of white light with a known intensity distribution as a function of wavelength. It falls on a sensor (your eye). How it is perceived (quantified) will depend on the response behavior of the sensor itself. The response behavior is a function of wavelength. So, the sensor will quantify the incoming light signal according to its own response curve.
Now imagine the white light source is reflected from a mirror. How it is reflected will depend on the reflectivity of the mirror. The reflectivity is a function of wavelength. A perfect mirror will have a reflectivity of unity across all wavelengths. The mirror will transmit an intensity distribution pattern that is different from the incoming white light source depending on the degree to which its transmission function is not perfect.
Now, imagine the reflected light is sent to the sensor. The sensor will process this reflected incoming light signal using its own response curve.
- A white light source has its own transmission pattern.
- A sensor has its own response curve.
- A mirror has its own reflectivity curve.
The combined system of source + mirror + sensor is only the same as the system source + sensor when the mirror has a perfect reflectivity curve (unity over all wavelengths).
Short answer: No. Light is light.
According to prevailing theories, there is no distinction between photons of the same wavelength/frequency/energy, even if they have come from different sources or indirectly. If you accept that we perceive via our eyes, and that our eyes convert light into a biochemical signal, and that any epistemological perception events happen after than conversion, then, no, we do not perceive reflectors and emitters differently.
In practice, yes, something reflecting light will look different from something emitting it. You could probably engineer a reflecting object to look arbitrarily similar to an emitting object (provided the right lighting), but it would be hard.