We present high-field (<50 T) photoluminescence measurements of the binding energy of the singlet and triplet states of the negatively charged exciton in a 200-Angstrom quantum well. Comparing our data with those of other groups and with theoretical predictions we clearly show how the singlet, "bright" and "dark" triplet states may be identified according to the high-field dependence of their binding energies. We demonstrate that a very consistent behavior of the binding energy in a magnetic field has been observed in quantum wells of different widths by different groups and conclude that the triplet state found in this, as well as nearly all other experiments, is undoubtedly the bright triplet. By combining our data with that in the literature we are able to present the generic form of the binding energy of the spin states of the charged exciton in a magnetic field, which reveals the predicted singlet to dark triplet ground state transition at about 20 T.