Elvis impersonators have many similarities, such as long black sideburns
and rhinestone-studded suits, that are not inherited. In the same way, biological similarites are not always due to inheritance.
For example, look
at the skulls below. They belong to extinct animals, and both of them have
saberteeth long, ferocious canines. Would you guess that these saberteeth are
homologous inherited from a common ancestor with extra-long saberteeth?
These two skulls certainly look like the animals could have inherited their
saberteeth from a common ancestor. And the presence of canine teeth themselves is definitely a homology, in that the common ancestor of these two had canine teeth.
However, despite their similarities, the unusual length of these teeth is NOT homologous. One skull belongs to Thylacosmilus, a marsupial
mammal. The other belongs to Smilodon, the saber-toothed cat, which is a placental
mammal. Marsupial and placental mammals are very different, and diverged from each other a long time ago on the evolutionary tree.
Thylacosmilus is more closely related to other marsupials such as kangaroos and
koalas than it is to Smilodon. Smilodon is more closely related to other
placentals such as housecats and elephants than it is to Thylacosmilus. Saberteeth is not a common trait in the marsupials closely related to Thylacosmilus, or the placentals closely related to Smilodon.
Their common ancestor certainly had canine teeth, but they were probably not adapted into fierce "sabers."
As they weren't inherited from a common ancestor, the saberteeth in Smilodon and Thylacosmilus evolved independently from one another.
That means that one lineage on one part of the tree of life evolved saberteeth from normal length teeth, and a different lineage somewhere else on the tree also evolved saberteeth from normal length teeth.
These saberteeth are analogous structures.