Traits are "given" to animals by their ancestors. Or you can say animals inherit their traits from their ancestor. Of course, new traits can also evolve by modifying an existing trait. Unrelated animals by definition cannot receive the same trait from a common ancestor. Unrelated animals can independently evolve similar or analogous structures that originated in their different ancestors. For example, an octopus evolved its eyes independently of a frog, because their common ancestor did not have eyes. The frog eye and the octopus eye are therefore known as analogous structures. OTOH, the frog eye, the bird eye, the cow's eye and the human eye are all inherited from the common ancestor of frogs, birds, cows, and humans. That ancestor has eyes. The eye of frogs, birds, cows, and humans are known as homologous structures.
When a trait becomes useless, it is usually known as a vestigial structure, because they usually deteriorate due to a lack of natural selection that weeds out the non-functional versions. An example of a useless or vestigial structure is the pelvic and rear limb bones of whales. The pelvic and rear limb bones found in some snakes are also useless and vestigial. However, snakes and whales (though distantly related) did not inherit these vestigal structures from a common ancestor.They instead inherited fully functional, non-vestigial limbs and pelves from that common ancestor, which is a primitive reptile, known as an anapsid reptile, that had 4 fully functional legs and fully functional pelvic bones. Therefore the vestigial pelvis and rear limb bones of snakes and whales are both analogous structures and homologous structures. They are considered homologous since they inherited leg and pelvis bones from a common ancestor, but since they became vestigial independently, their vestigial nature is considered analogous. Hope I haven't confused you too much.
I think you're talking about two different things, vestigial traits and analogous traits. Traits possessed by related animals are called homologous.
I forgot the name, When traits are given to unrelated animals? whats the word?
