A homologous trait shared between two species is actually the same thing as synapomorphy, but synapomorphy is the term favored in modern biology. Both terms refer to similarities between different species that derive from a common ancestry. Similarities between species that are not from shared ancestry are called convergent traits.
The term "homology" was first used by Robert Owen, a comparative anatomist in the 1800s who particularly noticed the similarities in the forelimbs of vertebrate animals. Every vertebrate forelimb has similar structures and arrangements of bones. Charles Darwin later suggested that these similarities were due to common ancestry. The change from the use of homology to synapomorphy was because the former was used before the development of evolutionary theory. The latter term is used only by scientists with that perspective, and so its meaning incorporates evolutionary concepts.
Any trait that qualifies as a synapomorphy is one that is shared within the descendants of a common ancestor, but not with other groups. The wing of a bat and the wing of a bird have very different arrangements of bones, despite similar external shapes. Since the similarities do not arise from a common ancestor, they are an example of convergent evolution, not synapomorphy.