First of all, you must know that Vietnamese is really clear thinking about other nations and past events. We know about Japan and Japanese in different eras and different contacts, and are very clear about those.
The first contact should be from the ancient dynasties, where Vietnamese people and governments knew about Japan with the name “Phù Tang”, a nation far east of the sea. Their businessmen crossed the sea and traded with Vietnamese in ports like Hội An, and there was a Vietnamese princess who get married to a Japanese lords and moved there. As far as I know, this relationship ended when both Vietnam and Japan chose to close their international trade market. So all we now know about ancient Japan, is through TV shows, history lessons, and sometimes anime/manga. I think in ancient times, Vietnam and Japan were quite the same: poor agricultural nation, full of uneducated farmers.
The second contact is after the French came and colonized Vietnam, while Japan was under Meiji era and developed so fast. A Vietnamese patriot named Phan Bội Châu chose to find supports from Japan, whom he believed “had the same red blood and yellow skin” as Vietnamese, and they could help Vietnam liberate. He gained some agreements and wills to help from some Japanese friends, whom he could only communicate through letters in Sino-centic language, but they helped him moved Vietnamese students to Japan to study. This campaign was called Đông Kinh Nghĩa Thục, with Đông Kinh means Tokyou. Phan Bội Châu had hoped that the well-educated students can come back and help Vietnam developed, but sadly this campaign was interrupted by the French and Japan governments. This also ended a really good friendship that the two countries once had.
The third contact is really sad. Vietnam was still under French colonization and Japan became nacist. Then World War II, and Japan took over Vietnam from the French. This happened in 1945, and the nacist Japan caused a serious famine in Vietnam and it killed 2 millions people. Then the nacist Japan lost the World War, and Viet Minh gained the country from them.
And the fourth contact, is recently. Now Vietnam and Japan became business partners. Many Vietnamese youngsters know about Japan through manga (with Doraemon as the first manga ever to be published in Vietnam), anime, and other entertainment products. Then we know more about Japan, for example their tea cultures, sushi, samurai and ninjas, and so on. Hope that the relationship would go well.
About the feels of similarites, I have to disagree with all of the others. Vietnamese nowaday doesn’t any similarities with Japan, or at least most of the cases. Yes, tea culture feels similar, but Kanji is not something we can understand or even feel familiar. Both countries have Buddhism, but they’re far from being similar. While Japanese monks can eat meats and marries, Vietnamese monks can’t. While Ashura is a famous god killer in Japanese culture, the Vietnamese version A tu la is not that well-known. The Haiku poems are too exotic and not familiar. The last names don’t even make sense. The Kings are not really the kings, and their language is so strange. The Samurais just have too much of self-pride that Vietnamese will wonder how dumb they are to commit suicide (seppuku). Even in general East Asia, Japanese culture is too exotic and foreign that it doesn’t really belong here. They were isolated in the islands and developed a really unique culture, and it’s hard to say Vietnamese can feel familiar with them, nor the Japanese can either way.
But after all, the relationship between the two is now ok. Better understanding makes better life.