Serum hemoglobin is a blood test that measures the level of free hemoglobin in the liquid part of the blood (the serum). Free hemoglobin is the hemoglobin outside of the red blood cells. Most of the hemoglobin is found inside the red blood cells, not in the serum.
Hematocrit is a blood test that measures the percentage of the volume of whole blood that is made up of red blood cells. This measurement depends on the number of red blood cells and the size of red blood cells.