A horse named Secretariat won the Triple Crown in 1973. Other than that, I've never heard the word.
I think they are different words. "secretaría" is not even in the top 50,000 most frequent words in Spanish subtitles. I'm not 100% sure what "secretariat" means in English. It is not a common English word. http://www.merriam-webster.com/dictionary/secretariat "the administrative department of a governmental organization" is what it most likely means though. Undoubtedly it was a mistake to teach beginners this word.