Every story of a pet surfacing in another state/the other side of the country/months or years later, the pet was microchipped. So many cats have a superficial resemblance to each other that otherwise it would be neigh on impossible to identify them. I'm old enough to remember when cats and dogs had numbers tattooed in their ears, and I doubt Amber would have had that done if it were still the thing, either.
But take heart. While odds are that Rarity is dead, if she did wander miles and miles away and survive, then she'll find a new home. One of my childhood cats turned up on our doorstep bedraggled and starving, and the vet said that from the state of his paws, he'd wandered a long, long distance. No tattoo or collar or anything. He spent ten years with us and was the best goddam cat. RIP Marmalade.