HOMOLOGOUS:
In comparing two species such as the human and chimpanzee, you come to find a homologous trait. The tailbone of a human being and the tail of a monkey are great examples, in my opinion. The tailbone is actually called the tailbone because of this shared lineage. Because a human doesn’t actually have a tail but the tailbone is the last vestige or remains of where a tail would be, it is referred to as “vestigial.” Humans used to have a tail, but eventually evolved out of it, leaving behind the reminisce of simply the tailbone, whereas chimpanzees still carry that trait, as well as the tailbone. Humans and chimpanzees, two very closely related species, share a common ape-like ancestor that of which lived on Earth millions of years ago.
Above is a photograph of a human tailbone.
Above is a photograph of a chimpanzee's tailbone.
ANALOGOUS:

In comparing two different species such as, a human Eye and an Octopus Eye we find analogous traits. Both a human and octopus share not only different diets but also different environments. The octopus and the human are not closely related, whatsoever, yet the eye of a human is very similar in structure to the eye of the octopus. In fact, the octopus eye is superior to the human eye in that it does not have a "blind spot". Both eyes are round and have the same structural traits. Both have an eyelid, cornea, retina, pupil, iris, lens, and optic nerve. The human eye and octopus eye are used to hunt for prey in two completely different environments. Being underwater the octopus must be able to see in the dark, while the humans must be able to see in bright habitats. This can be the reason why both species developed an eye to help advance its survival in habitats they live in. I would presume that millions of year ago they shared a common ancestor between the octopus and human had analogous traits. The species had to of, because when the ancestral organisms split and down the path of evolving into each species and giving them the ability to develop eyeballs evolved into every species following to also develop eyeballs, regardless of their function, location, or lifestyle.