Homolog: A gene related to a second gene by descent from a common ancestral DNA sequence. The term "homolog" may apply to the relationship between genes separated by speciation (ortholog), or to the relationship between genes originating via genetic duplication (paralog)
Ortholog: Orthologs are genes in different species that have evolved from a common ancestral gene via speciation. Orthologs often (but certainly not always) retain the same function(s) in the course of evolution. Thus, functions may be lost or gained when comparing a pair of orthologs.
Paralog: Paralogs are genes produced via gene duplication within a genome. Paralogs typically evolve new functions or else eventually become pseudogenes.