A modern NMR spectrum usually examines the region between delta=-20*"ppm" to 230*"ppm", i.e. 250*"ppm" in the ""^13C{""^1H} NMR spectrum. I think that you could reasonably report a ""^13C{""^1H} "NMR" to 0.1*"ppm" resolution. And so there are approx. (250*"ppm")/(0.1*"ppm")=2500........
And so by this reasoning there are 2500 individual ""^13C{""^1H} "chemical shifts".....Usually, different spectrometers give slightly different "NMR chemical shifts........" for the same compound.
Most of the time, when we examine a ""^13C{""^1H} "spectrum" we are more interested in the number of signals we see, i.e. whether the proposed structure is consistent with the number of ""^13C signals observed, rather than trying to assign each signal to a particular carbon. Of course, there are a raft of higher end experiments you can perform, hoesy, roesy, nosy, hohohaha, hetcorr, hmqc, hmbc etc....
