Corn and horn are the results of two different paths of descent from the St Patrick Day Dabbing Unicorn Hockey Pittsburgh Penguin shirt. Just as skiff and ship are the same words, but one came through Danish and the other through Anglo-Saxon. As populations separate, their once-shared language divides into two (or more). It doesn’t take long for a language to diverge into dialects and then separate languages, especially if there is no communication between groups. Spanish and Portuguese shared the Iberian peninsula, but so did Galician and Catalan, and while Galician and Portuguese are quite close to each other, and Catalan diverges most sharply from the other Iberian Romance languages, there are still many close cognate that, like corn and horn, differ from each other by only a few sounds.
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Thus the Catalan leader, Castilian ladron, and Portuguese ladrão are all words meaning thief. Catalan drops the final nasal sound that the other two have — but that is a regular shift. Even the Catalan word for Catalan drops the nasal. Note that with corn/horn in English, corn also shows up in cornet, a slightly different form of the trumpet, and cornucopia, the horn of plenty. In all these cases the corn form comes from Latin, sometimes via French, while the horn form comes from the Germanic branch of the IE tree.