The primary use of cytochrome is as a vital component of the ATP synthesis process, which sustains life, in the mitochondria.
Whereas red blood cells include a protein called haemoglobin, which distributes oxygen to your body's organs and tissues while returning carbon dioxide to your lungs.
Haemoglobin isn't a cytochrome at all.
Redox catalysis is the primary function of cytochromes, in which the iron in the heme core is interconverted between Fe(II) and Fe(III) states.
Haemoglobin's primary function is to bind and transport oxygen.
It cannot mix with oxygen in the ferric state (FeIII).
The heme group of cytochrome and haemoglobin share the same Fe porphyrin ring structure.