Two metrics on a manifold are said to be (pointwise) projectively related if their geodesics are same as point sets. Projectively related Einstein metrics are related by a simple ODE along geodesics. In particular, if they are complete with negative Einstein constants, then one is a multiple of another. There are many Einstein metrics that are projectively isolated. Metrics under our consideration are not assumed to be Riemannian. Projectively flat metrics on Rⁿ are those whose geodesics are straight lines. Projectively flat Riemannian metrics must be of constant curvature. However, there are many non-Riemannian projectively flat metrics of constant curvature such as Hilbert metrics and Bryant metrics, etc.