  We revisit four approaches to the BiTangential Operator Argument
Nevanlinna-Pick (BTOA-NP) interpolation theorem on the right half plane: (1)
the state-space approach of Ball-Gohberg-Rodman, (2) the Fundamental Matrix
Inequality approach of the Potapov school, (3) a reproducing kernel space
interpretation for the solution criterion, and (4) the
Grassmannian/Kre\u{\i}n-space geometry approach of Ball-Helton. These four
approaches lead to three distinct solution criteria which therefore must be
equivalent to each other. We give alternative concrete direct proofs of each of
these latter equivalences. In the final section we show how all the results
extend to the case where one seeks to characterize interpolants in the
Kre\u{\i}n-Langer generalized Schur class $\cS_{\kappa}$ of meromorphic matrix
functions on the right half plane, with the integer $\kappa$ as small as
possible.
