Affinity is an ability that has been printed on a small number of cards. The only one of these that the current Modern Affinity decks seem to run is Thoughtcast and even that does not appear in all of them. So, why is this deck called affinity when it potentially runs no cards with the "affinity" ability? Why not "metalcraft", calling out Mox Opal, Etched Champion, and Galvanic Blast? Why not "robots", which seems to be another name for the affinity deck that hasn't caught on?
It is almost certain that the deck is meant to be the spiritual successor to the old Mirodin-era affinity deck that also used Thoughtcast, Arcbound Ravager, Cranial Plating, Darksteel Citadel, and Blinkmoth Nexus (pretty much everything else about the Modern affinity deck is different), but in what way is it the spiritual successor?
In what the deck does in general. The name "affinity" at this point refers to the "for each artifact you control" aspect of the "affinity for artifacts" ability, leveraged by Cranial Plating and Master of Etherium. At this point, players think of affinity as just being more powerful for having more artifacts rather than the literal affinity ability.
Card overlap. There are enough key cards in common that players think of the decks as the same thing. Arcbound Ravager and Cranial Plating are enough for people to say, "Yup, that's an Affinity deck."
There was actually a somewhat continuous evolution of the Mirodin-era affinity deck into the deck's current form (as new sets were released and Modern replaced Extended), and no one happened to rename the deck when Frogmite and Myr Enforcer got cut.
