False friends is better. Cognates is a bit more specific, referring to words that have the same root. There can be cognates within a language, (language and linguistics, for example), and cognates between languages. (independence, independencia) Some of these mean the same or similar things, others mean different things, or even the opposite thing, to the word that seems the same,. Sometimes, also, there are words that look alike but aren't from the same root.
I'm not sure why you'd call it a false friend. I can't think of any English words that appear similar with a different meaning. The closest word familiar to English speakers would be the Latin nova that means new. Nuevamente isn't a false friend of nova because again effectively means a new time.
In my family(Guatemalan-Puerto Rican blend) ¨Es verano nuevamente¨ is ONLY used in poetry or to be ¨polite¨For example, I got tired of being out during a company (softball)baseball game so I shouted to the blood-sucking vampire(vampire vs. umpire. What´s the difference!?)"You would have said I was safe if you would have had been wearing your glasses!" instead of ...if you would been wearing your glasses! My example is to prevent a fight, by not saying, "You four-eyed idiot. Why did we pick you for umpire, you freak!? You're as blind as a bat." but we are here to learn to speak Spanish ... correctly. I apolgize for going off on a tangent, my fellow students. P.S. I would use¨Es verano otra vez¨in everyday speech. I'm just saying. :^[}
Thanks. The way different dialects use expressions is interesting, I like the discussions, as long as we all recognize that one isn't necessarily more correct than another. I will say, that Spanish as it is taught is not the same as Spanish as it is spoken in normal, every day conversation. I constantly find myself using expressions, words, etc. that i've learned through reading or grammar books, that make my students laugh, and they use words, expressions, etc. that I simply don't understand until they use other words. Things like - it's a piece of cake translating to es pan comida, or the use in Northern Mexican Spanish of güero instead of rubio for blond, can be really confusing.