The opposite of homologous structures are analogous structures, which are similar structures between two taxa that were not present in the last common ancestor but rather, evolved separately.
An example of an analogous trait would be the wings of bats and birds, which evolved independently in each lineage after diverging from ancestors with forelimbs not used as wings (terrestrial mammals and theropod dinosaurs, respectively).
In the above example, the bird and bat wings are analogous as wings, but homologous as forelimbs because the organ served as a forearm (not a wing) in the last common ancestor of tetrapods .
The wings of a maple seed and the wings of an albatross are analogous but not homologous (they both allow the organism to travel on the wind, but they didn't both develop from the same structure).
In particular, they clarify whether certain traits are homologous (found in the common ancestor as a result of divergent evolution) or homoplasy (sometimes referred to as analogous: a character that is not found in a common ancestor, but whose function developed independently in two or more organisms through convergent evolution).
Previously, phylogenetic trees were constructed based on homologous and analogous morphology; however, with the advances in molecular biology, construction of phylogenetic trees is increasingly performed using data derived from molecular analyses.