Stellar electromagnetic signatures By using only the electromagnetic signature of a star, could a star be distinguished with reliable accuracy from any other star?
To elaborate a little, say we have a collection of about 200,000 stars. By using EM spectrum alone (and any means of analysis, such as spectral analysis), and by tagging each star with its corresponding EM signature, could there be similarities too close to fail a distinction between any two or more stars?  

Now, of course, I know that such a thing is possible. I'm not asking whether it is possible. I just want to know the odds of such a lack of distinction, considering all the factors of stellar evolution. It's either in the ballpark or not.
The spectrum of a star is almost certainly a unique fingerprint. Even though stars are born in clusters, formed from the reasonably chemically homogeneous environment of a giant molecular cloud, there are likely to be small differences in their local environment. Furthermore their formation environments, and the stars themselves at later times, can be polluted by external events (e.g. nearby supernovae). Even if their chemical abundances were identical, their spectra would not be because of differences in their mass, rotation and hence their temperatures.

But, the differences between stars may be smaller than the measurement precision, rendering their spectra effectively indistinguishable.

To give any sort of definitive answer requires some definition of what types of stars are being observed, their temperature, gravity and chemical abundance dispersion, at what spectral resolution and with what signal to noise ratio in what waveband.

At the moment I would say this is impossible for any star in our Galaxy. The differences in the spectra between one star and its most similar "twin" (the word might be appropriate here, as they were likely born in the same stellar nursery) are far smaller than we can distinguish with current data and techniques.