Heisenberg's contribution was to note that the mathematical formulation of this symmetry was in certain respects similar to the mathematical formulation of spin, whence the name "isospin" derives.
While the forms of these matrices are the isomorphic to those of spin, these Pauli matrices only acts within the Hilbert space of isospin, not that of spin, and therefore is common to denote them with τ rather than σ to avoid confusion.