  We compare two non-relativistic (NR) reduction schemes (heavy-fermion and
Foldy-Wouthuysen) that are used to derive low-energy effective-field-theory
Lagrangians. We give the explicit transformation between the two types of
fields to O(1/m^2), derived from a quite general, relativistic Lagrangian.
Beyond leading order the NR reductions always involve the smaller components of
the Dirac spinors that are to be integrated out to formulate the NR theory.
Even so, the transformation between the NR Lagrangians can be carried out
explicitly to O(1/m^2) using a field renormalization, as long as the lower
components of the Lagrangian are known. The fixed coefficient corrections to
some low-energy constants at O(1/m^2) will depend on the particular scheme
chosen, but will match after the field renormalization.
