I speak both, not wonderfully, but I do. I studied Japanese in college when I was in Japan for a couple of semesters and learned to carry on conversations. I also have a Japanese son in law who loves to speak to me in Japanese, and have been a Japanese professor. I also spent a year teaching English at a language school in Japan. They were my introduction to the Orient.
I spent 14 years in S. Korea. I studied Korean on my own and used what I studied to teach my Korean students to speak English. I always try to understand the language of my students because it helps them more if as a professor, I understand their grammar. I also have a Korean son in law, and it is his brother and parents who always speak to me in Korean because they can’t speak English. His brother has had me teaching Bible classes in Korean and translating movies for him.
As far as the difference in the grammatical patterns, I haven’t found any. The vocabulary is vastly different, but the word order is the same, the particles go in the same place, verbs and adjectives are both conjugated, “if” and “when” clauses are put together the same way, “because” is used the same way, etc.
They are two separate languages, but the two countries have been next door to one another every since they came into existence thousands of years ago. They have shared ideas about food, ideas about daily life, ideas about language, and even ideas about writing. However, the Koreans no longer use the Chinese characters the Japanese use. There are many things that I find they do the same, and my sons in law try to tell me who they think actually began certain things. The emperor of Japan is part Korean. When the guy from Osaka castle in Japan originally united all of Japan, he went to Korea next thinking they were enough alike the Japanese that they should be one country with the rest of them, but the Koreans wanted no part of it, and it never happened. However, Japan has occupied Korea. If you read stories of Korean history, they think of the Japanese as pests because they have come and made war on them so many times trying to take them over. They are like brothers and sisters who argue. They are close, but their languages are not the same. Neither did their languages come from the same base. They have just influenced one another a lot.