  Quantum entanglement is a particularly useful characterization of topological
orders which lack conventional order parameters. In this work, we study the
entanglement in topologically ordered states between two arbitrary spatial
regions, using two distinct mixed-state entanglement measures: the so-called
"computable cross-norm or realignment" (CCNR) negativity, and the more
well-known partial-transpose (PT) negativity. We first generally compute the
entanglement measures: We obtain general expressions both in (2+1)D
Chern-Simons field theories under certain simplifying conditions, and in the
Pauli stabilizer formalism that applies to lattice models in all dimensions.
While the field-theoretic results are expected to be topological and universal,
the lattice results contain nontopological/nonuniversal terms as well. This
raises the important problem of continuum-lattice comparison which is crucial
for practical applications. When the two spatial regions and the remaining
subsystem do not have triple intersection, we solve the problem by proposing a
general strategy for extracting the topological and universal terms in both
entanglement measures. Examples in the (2+1)D $Z_2$ toric code model are also
presented. In the presence of trisection points, however, our result suggests
that the subleading piece in the PT negativity is not topological and depends
on the local geometry of the trisections, which is in harmonics with a
technical subtlety in the field-theoretic calculation.
