Why are a bird wing and a bat wing homologous as forelimbs but not as wings?

In biology, the distinction between homology and analogy is fundamental to understanding evolutionary relationships.

The forelimbs of birds and bats are considered homologous because they share a common evolutionary origin. Both structures are derived from the forelimb bone structure of early terrestrial vertebrate ancestors. Despite their different modern functions, the underlying skeletal arrangement—including the number and placement of bones—is fundamentally similar, reflecting their shared ancestry.12

Conversely, the wings of birds and bats are considered analogous because the power of flight evolved independently in these two groups. Birds developed flight while evolving from early reptiles, whereas bats developed flight much later, after their mammalian ancestors had already diverged from reptiles. Because these structures evolved to perform the same function (flight) without being inherited from a common flying ancestor, they represent a functional similarity rather than an evolutionary one. In essence, while the "hardware" (the forelimb) is homologous, the "software" (the wing for flight) is an analogous adaptation that arose separately in each lineage.132