In biology, we would say that the wings of birds and insects are analogous because they have a common function. However, they are not homologous structures because they do not share a common origin in evolutionary history. A whale flipper, a human hand, and bat or bird wings are homologous structures because they share a common ancestry. Even some contemporaries of Charles Darwin used analogous relationships to classify organisms. Such schemes make an attractive display but tell us nothing about the underlying relationships between organisms.
Some salamanders are paedomorphic .
These salamanders delay development of body characteristics relative to sexual reproduction. As a result, they all look fairly similar, especially with respect to the exposed larval gill structures. At one time, they were all classified together because it was thought that the presence of the exposed gills and many other structures represented homologies. But, a more detailed analysis of their genetics shows that they simply look alike because they have all have delayed bodily development relative to sexual maturation. The exposed gills and many other structures are simply analogous characters.