Homologous vs. Analogous Traits

Homologous

Two species that carry a similar Homologous traits are cats and dogs, they both posses the paw trait. 

Both animals carry the homologous paw trait, although both species are completely different. Cats coming for the feline species and dogs from the canine species. Both animals differ on their body structures, dogs having a broad muscular structure and cats having a small and flexible structure. They both carry the same trait but use their paws for completely different things. A dog's paws are used to run faster, longer, and make sharper turns than most animals, they also use their paws to dig and bury things such as bones and other items. As for cats, they use their paws for cleaning themselves, climbing trees, and even when playing. Cats often try to catch thing with their mouth and paws when they chase things.

The common ancestor of cats and dogs would be the extinct mammalian carnivore called the Miacids, they gave rise to cats, bears, dogs, skunks, mongooses, hyenas, and all other felids (ancestor of the feline family) and canids (ancestor of the canine family).

Analogous

Both the human and octopus eye are very similar and is considered a analogous trait.

The human eye and the eye of an octopus are almost identical, the only difference being that the human eye has a blind spot. For example, if you close your right eye, look at the "L" with your left eye, and the "R" will disappear (if close enough). 

              R                                             L

As for the octopus eye, it has no blind spot. Both of these species are similar, the only difference being the blind spot.

The common ancestor of a human and an octopus would be found 700 million years ago, a wormlike creature with eyespots. This creature's eye wasn't as complex or as developed as ours.