The paper revisits the advertising differential game suggested by G. Leitmann and W. E. Schmitendorf in their paper "Profit Maximization Through Advertising: A Nonzero Sum Differential Game Approach", IEEE Transactions on Automatic Control , AC-23, 645--650, 1978. We put the model into perspective and discuss the related issues of (i) state separable (or linear state) games and (ii) open-loop equilibria that are feedback equilibria which are constant with respect to state.