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Coming to your question, Fertilin and Fertilizin are different.
Fertilin is a sperm surface protein with an essential role in fertilization. It is required for the migration of spermatozoa through the oviduct, for binding to the zona pellucida, and for efficient binding to the egg plasma membrane. Fertilin consists of two subunits, fertilin alpha and beta, both of which belong to the metalloprotease-disintegrin protein family (ADAMs). Fertilin alpha and beta are made as larger precursors that are processed proteolytically at different stages of sperm maturation in the testis and epididymis. Fertilin alpha is processed first, most likely by a pro-protein convertase in the secretory pathway of testicular cells. Fertilin beta is processed later, while spermatozoa are in transit through the epididymis.(taken from this reference 1) Thus this protein is present in Sperm.
Fertilizin is sperm-agglutinating substance (glycoproteins) present on Zona pellucida layer of the egg surface. Antifertilizin-fertilizin complex play a key role in sperm penetration. (Have a look at reference 2 &3 ). Thus, Fertilizin is present on egg surface.
Now look back at the images you provided with your question. Role of Ferilizin and fertilin-beta are clearly given.