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New and/or corrected 800 MeV p + """"Ca elastic angular distributions are presented. The data, together with analyzing power measurements, are analyzed to investigate the isotopic neutron and matter density differences between these four calcium isotopes. The analysis employs a local, spin-dependent form of the second order Kerman, McManus, and Thaler optical potential in which approximately model-independent forms for the neutron densities are assumed. Nucleon-nucleon amplitude uncertainties which occur at 800 MeV are taken into account in determining the empirical isotopic density differences. The deduced neutron and matter density differences are compared to the results of other intermediate energy proton and alpha particle scattering analyses and to Hartree-Fock predictions. The various empirical results are generally in good agreement with each other and with the Hartree-Fock predictions, except for "Ca where the results obtained here and elsewhere suggest that the "Ca neutron excess is not distributed at quite as large a radius as predicted by Hartree-Fock theory.NUCLEAR REACTIONS Proton elastic scattering cross sections; targets, Ca; Ei, b=800 MeV; second order Kerman, McManus, and Thaler optical potential; neutron and matter isotopic density differences.