What is the difference between oxyhemoglobin and hemoglobin?

The same but....: Each hemoglobin molecule is able to carry 4 oxygen molecules. The iron atom in the hemoglobin enables it to bind to the oxygen. As blood passes through the lungs, it is exposed to oxygen and become oxygenated hence Oxyhemoglobin as the blood passes in tissues, it gives away the oxygen and becomes de oxygenated. Hence DeOxy hemoglobin

With and without: oxygen. Hemoglobin is the red, iron containing protein in blood. When it binds oxygen, it takes a slightly different character, e.g. is more red, and is called oxyhemoglobin. Other variants are methhemoglobin, carboxyhemoglobin.