A cognate is a word in one language related to a similar word in another related language by a common ancestor. "lunar" in English is related to Spanish "luna", French "lune", and Portuguese "lua", for example. "lunar" means "having to do with the moon" and the Spanish, French, and Portuguese words cited all mean "moon". All these words are directly or indirectly related to their common ancestor in Latin "luna". Cognates can only occur between related languages. English is related to many Western European languages, Greek, Persian, Hindi and Sanskrit, but the languages of Asia developed in a different, unrelated language family, and so have no cognates with English.
A false cognate is a pair of words which appear to have the cognate relationship, and may in fact be cognates in some indirect way, but have no similarity of meaning.
"pretend" in English means something completely different from "pretend" in French (as well as being pronounced quite differently, of course).
"gift" in English means something completely different from "Gift" in German.
"exit" in English means something completely different from "exito" in Spanish.
These are examples of false cognates.