  Non-relativistic string theories promise to provide simpler theories of
quantum gravity as well as tractable limits of the AdS/CFT correspondence.
However, several apparently distinct non-relativistic string theories have been
constructed. In particular, one approach is to reduce a relativistic string
along a null isometry in target space. Another method is to perform an
appropriate large speed of light expansion of a relativistic string. Both of
the resulting non-relativistic string theories only have a well-defined
spectrum if they have nonzero winding along a longitudinal spatial direction.
In the presence of a Kalb--Ramond field, we show that these theories are
equivalent provided the latter direction is an isometry. Finally, we consider a
further limit of non-relativistic string theory that has proven useful in the
context of AdS/CFT (related to Spin Matrix Theory). In that case, the
worldsheet theory itself becomes non-relativistic and the dilaton coupling
vanishes.
