  Recently, it has been proposed that space-based atomic sensors may be used to
detect gravitational waves. These proposals describe the sensors either as
clocks or as atom interferometers. Here, we seek to explore the fundamental
similarities and differences between the two types of proposals. We present a
framework in which the fundamental mechanism for sensitivity is identical for
clock and atom interferometer proposals, with the key difference being whether
or not the atoms are tightly confined by an external potential. With this
interpretation in mind, we propose two major enhancements to detectors using
confined atoms, which allow for an enhanced sensitivity analogous to
large-momentum-transfer (LMT) used in atom interferometry (though with no
transfer of momentum to the atoms), and a way to extend the useful coherence
time of the sensor beyond the atom's excited state lifetime.
