  We relate the (anisotropic) variable coefficient local and nonlocal
Calder\'on problems by means of the Caffarelli-Silvestre extension. In
particular, we prove that (partial) Dirichlet-to-Neumann data for the
fractional Calder\'on problem in three and higher dimensions determine the
(full) Dirichlet-to-Neumann data for the local Calder\'on problem. As a
consequence, any (variable coefficient) uniqueness result for the local problem
also implies a uniqueness result for the nonlocal problem. Moreover, our
approach is constructive and associated Tikhonov regularization schemes can be
used to recover the data. Finally, we highlight obstructions for reversing this
procedure, which essentially consist of two one-dimensional averaging
processes.
