  In the original Collins-Soper-Sterman (CSS) presentation of the results of
transverse-momentum-dependent (TMD) factorization for the Drell-Yan process,
results for perturbative coefficients can be obtained from calculations for
collinear factorization. Here we show how to use these results, plus known
results for the quark form factor, to obtain coefficients for TMD factorization
in more recent formulations, e.g., that due to Collins, and apply them to known
results at order $\alpha_s^2$ and $\alpha_s^3$. We also show that the
"non-perturbative" functions as obtained from fits to data are equal in the two
schemes. We compile the higher-order perturbative inputs needed for the updated
CSS scheme by appealing to results obtained in a variety of different
formalisms. In addition, we derive the connection between both versions of the
CSS formalism and several formalisms based in soft-collinear effective theory
(SCET). Our work uses some important new results for factorization for the
quark form factor, which we derive.
