  The sectorized description of the (chiral) heterotic string using pure
spinors has been misleadingly viewed as an infinite tension string. One
evidence for this fact comes from the tree level 3-point graviton amplitude,
which we show to contain the usual Einstein term plus a higher curvature
contribution. After reintroducing a dimensionful parameter $\ell$ in the
theory, we demonstrate that the heterotic model is in fact two-fold, depending
on the choice of the supersymmetric sector, and that the spectrum also contains
one massive (open string like) multiplet. By taking the $\ell\to\infty$ limit,
we finally show that the ambitwistor string is recovered, reproducing the
unexpected heterotic state in Mason and Skinner's RNS description.
