This paper compares the classical concept of assumed density filters (ADF) with a new class of approximate filters, the projection filters (PF). It is shown that the concept of ADF is inconsistent in the sense that the resulting filters vary according to the choice of a stochastic calculus, i.e. Itô or McShane-Fisk-Stratonovich (MFS). The PF are based on the differential geometric approach to statistics and are well defined. It is shown that in the context of the exponential families, the PF coincide with MFS-based ADF. An example is provided, which shows that this does not hold in general, for non-exponential families of densities.