Formulations of heterotic strings, that involve twistor-like variables and are invariant under N-extended world-sheet supersymmetry, have been proposed recently. Here we show that in suitable partial gauges these twistor-string models, at least for N = 1, give rise to the Green-Schwarz, non-gauge-fixed, heterotic string on one hand and, on the other hand, to the Neveu-Schwarz-Ramond one.