In the simplest Matérn point processes one retains certain points of a Poisson point process in such a way that no pairs of points are at distance less than a threshold. This condition can be reinterpreted as a threshold condition on an extremal shot-noise field associated with the Poisson point process. This paper is focused on the case where one retains points that satisfy a threshold condition based on an additive shot-noise field of the Poisson point process. We provide an analytical characterization of the intensity of this class of point processes and we compare the packing obtained by the extremal and additive schemes and certain combinations thereof.