Both of these families are part of Indo-European, for which the Ethnologue web page lists 425 languages!
When accompanied by splits of populations, language change results first
in dialect divergence (the kinds of differences we see between British and
American English; between the French of France and of Quebec; between New
World and Old World Spanish and Portuguese). Over longer time periods, we
see the emergence of separate languages as in the contemporary Romance languages,
separated by about 2000 years, and the Germanic languages, whose divergence
began perhaps 500 years earlier. Both of these families are part of Indo-European, for which the Ethnologue web page lists 425 languages! Though political
considerations often intervene in whether a particular speech variety is
considered to be a language or a dialect, the basic idea behind linguistic
classifications is that dialects are mutually intelligible, whereas languages
are not.