  The one-loop QCD heavy quark potential is computed to order v^2 in the color
singlet and octet channels. Several errors in the previous literature are
corrected. To be consistent with the velocity power counting, the full
dependence on |p' + p|/|p' - p| is kept. The matching conditions for the NRQCD
one-loop potential are computed by comparing the QCD calculation with that in
the effective theory. The graphs in the effective theory are also compared to
terms from the hard, soft, potential, and ultrasoft regimes in the threshold
expansion. The issue of off-shell versus on-shell matching and gauge dependence
is discussed in detail for the 1/(m k) term in the potential. Matching on-shell
gives a 1/(m k) potential that is gauge independent and does not vanish for
QED.
