orthologs are copies of the same genes within the same species.
This is wrong. By definition, orthologs are genes derived from a speciation event, paralogs are derived from a duplication event. Orthologs are what is usually meant when people talk about "the same gene in different species". Homologs are genes that derive from the same ancestor (= orthologs+paralogs). Formally, these relationships can only be inferred from a phylogenetic tree although short cuts and approximations are often used for computational reasons. How much effort should go into assembling gene families depends on how much one cares about the evolutionary history of the genes.