The application of the divided difference of a function to the inhomogeneous symmetric functions (factorial Schur functions) of Biedenharn and Louck is shown to head to new relations and simplified proofs of their properties. These results include determinantal definitions and the factorial Jacobi-Trudi identities with extensions to skew versions. Similar properties of a second class of sym-metric functions depending on an arbitrary parameter, and of importance for generalized hypergeometric functions and series, are shown also to be derivable from the divided difference notion, slightly extended.