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We numerically examine the flow of disks moving through an array of obstacles.  At low obstacle densities the flow is is arrested when the system approaches the defect-free jamming density known as point J. With increasing obstacle density, the disk density of the jamming point is reduced in a manner that is controlled by the criticality of point J. We observe that that at high obstacle densities, the behavior changes over to what we call clogging where the system forms a heterogeneous state with a pronounced memory effect and a diverging time scale near a critical obstacle density. The jammed states can be characterized as forming uniform robust states, while clogging forms a heterogeneous fragile state.  We discuss how these results can be applied to granular media, colloids, vortices and other particle like systems in the presence of disorder landscapes [Crossover from jamming to clogging behaviours in heterogeneous environments, H. Peter, A. Libal, C. J. Olson Reichhardt, and C. Reichhardt, Sci. Rep. 8, 10252 (2018); Clogging and jamming of colloidal monolayers driven across disordered landscapes, R. L. Stoop  and P. Tierno, Commun. Phys. 1, 68 (2018)].