Cortex: The intervening layer of the hair (i.e., between the cuticle and the medulla). It is made of spindle shaped cell and pigment granules (these give color to the hair). You may also find ovoid bodies (look like large pigment granules) and cortical fusi (small bubble-like structures) in the cortex.
Medulla (from the Latin for "marrow"): The innermost layer of the hair. It is made of cells that form a shaft through the middle of the hair. Different amounts of medulla may be present in the hair.