How did Spanish and Portuguese become so different despite being based off of the same language and having no major geographic barriers separating them?

While there's always room for more discussion, perhaps these two previous threads on related topics will be a good starting point:

/u/Miodi discusses the origins of the Portuguese and Spanish languages, which I think might yield some insights into the topics;

and /u/racms discusses the history of the Portuguese and Spanish identities, with follow-up questions and answers about the languages.