Accreted ice retains and preserves traces of the ocean from which it formed. In this work we study two classes of accreted ice found on Earth—frazil ice, which forms through crystallization within a supercooled water column, and congelation ice, which forms through directional freezing at an existing interface—and discuss where each might be found in the ice shells of ocean worlds. We focus our study on terrestrial ice formed in low temperature gradient environments (e.g., beneath ice shelves), consistent with conditions expected at the ice-ocean interfaces of Europa and Enceladus, and highlight the juxtaposition of compositional trends in relation to ice formed in higher temperature gradient environments (e.g., at the ocean surface). Observations from Antarctic sub-ice-shelf congelation and marine ice show that the purity of frazil ice can be nearly two orders of magnitude higher than congelation ice formed in the same low temperature gradient environment (~0.1% vs. ~10% of the ocean salinity). In addition, where congelation ice can maintain a planar ice-water interface on a microstructural scale, the efficiency of salt rejection is enhanced (~1% of the ocean salinity) and lattice soluble impurities such as chloride are preferentially incorporated. We conclude that an ice shell which forms by gradual thickening as its interior cools would be composed of congelation ice, whereas frazil ice will accumulate where the ice shell thins on local (rifts and basal fractures) or regional (latitudinal gradients) scales through the operation of an “ice pump”.