Is there any difference between these three?or these are just three names of same theorem?
Sampling operation has its roots in the mathematical interpolation theory which was used to generate certain function values at specified points from the availabe set (the samples) of existing values. These kind of work is summarized as Whittaker interpolation. Lagrange interpolation is also another related concept.
Sampling theorem in electrical engineering, however, has its roots in the communication engineering literature and pioneered by communications engineer Harry Nyquist, who was among the first to consider digital transmission of analog signals. The Nyquist sampling theorem states the minimum number of uniformly taken samples to exactly represent a given bandlimited continuous-time signal so that it (the signal) can be transmitted using digital means and reconstructed (exactly) at the receiving end.
Later, C.E.Shannon also worked on communications theory (especially the digital one) more from a probabilitistic point of view and published his conclusions as Information Theory within his classic paper of The Mathematical Theory of Communications. Among the works shannon did also include a more in depth analysis of sampling operation and resulting Shannon Sampling theorem which is identical to Nyquist sampling theorem for bandlimited signals.
Hence the uniform sampling of bandlimited continuous-time signals is referred to as Nyquist-Shannon sampling theorem. You may omit the inventors' names and simply call it sampling theorem remembering that it's the uniform sampling of bandlimited signals.