You should also know mechanistically what the spleen "filter" does. The cords of Bilroth in the spleen are basically narrow channels that mimic capillary networks in the periphery. The point is to test where the RBCs have the membrane flexibility needed to transit the capillary networks without getting stuck. Those that are not flexible enough will either have bulges sticking out (think about squeezing a fat man into a small pair of jeans) or be completely blocked. The parts that stick out will then be engulfed by macrophages (to generate bite cells) or the whole cell will be engulfed (leading to hemolysis, as in HS). Both sickle cell and HS can be explained using this model:
1) In sickle cell, the sickled RBCs in the periphery would not be flexible enough and thus would become stuck at branch points or within the capillaries themselves and block perfusion. The result would be pain crises and autoamputation in severe cases which you see in sickle cell patients. Because the spleen is designed to mimic this as a "filter" test, the same thing happens where sickle cells become stuck in the spleen and cut off circulation. Because the spleen filters a lot of blood, this will happen on a chronic basis and the decrease in splenic perfusion would then lead to atrophy.
2) In HS, the RBCs gradually lose plasma membrane (because the cytoskeletal anchoring system is defective) until they take on a spherical shape. This means they no longer have the extra membrane needed to be flexible enough to pass through the capillaries. Again, the spleen mimics this so the spherocytes become stuck in the spleen. However, because spherocytosis is a genetic condition that affects all RBCS at all times (unlike sickle cells which sickles usually only in low O2 conditions), there will be a lot more RBCs affected at any one time and they all accumulate in the spleen, leading to an enlarged spleen.