As one of the most specific, yet most diverse of human behaviors, language is shaped by both genomic and extra-genomic evolution. Sharing methods and models between these modes of evolution has significantly advanced our understanding of language and inspired generalized theories of its evolution. Progress is hampered, however, by the fact that the extra-genomic evolution of languages, i.e. linguistic evolution, maps only partially to other forms of evolution. Contrasting it with the biological evolution of eukaryotes and the cultural evolution of technology as the best understood models, we show that linguistic evolution is special by yielding a stationary dynamic rather than stable solutions, and that this dynamic allows the use of language change for social differentiation while maintaining its global adaptiveness. Linguistic evolution furthermore differs from technological evolution by requiring vertical transmission, allowing the reconstruction of phylogenies; and it differs from eukaryotic biological evolution by foregoing a genotype vs phenotype distinction, allowing deliberate and biased change. Recognising these differences will improve our empirical tools and open new avenues for analyzing how linguistic, cultural, and biological evolution interacted with each other when language emerged in the hominin lineage. Importantly, our framework will help to cope with unprecedented scientific and ethical challenges that presently arise from how rapid cultural evolution impacts language, most urgently from interventional clinical tools for language disorders, potential epigenetic effects of technology on language, artificial intelligence and linguistic communicators, and global losses of linguistic diversity and identity. Beyond language, the distinctions made here allow identifying variation in other forms of biological and cultural evolution, developing new perspectives for empirical research.