Studying noncompact manifolds with a flatness property, there is the notion of an asymptotically Euclidean manifold, and there is the notion of an asymptotically flat manifold which is defined in terms of curvature decay. Asymptotically Euclidean manifolds are asymptotically flat, but we shall see that in dimension 4 there exists an asymptotically flat example that is not asymptotically Euclidean.