You learn something new everyday! I didn't know the buddhists used a different type of swastika. It is indeed a mirrored version of the hindu one. In the image, the top right is hindu swastika, bottom left the buddhist one, and the bottom right the nazi one

It's not that even the hindus were the originators of the symbol. Archaeological evidence suggests that it was being used in 13000 BC, long before the Hindu religion came into being.. It was considered a good luck charm in 1900s, which is probably part of the reason why the Nazis adopted it. In fact, I saw many logos of societies of the time that used the swastika in creative ways. I will post them when I find them.
As for the Nazis stealing the icon, here is a great answer by someone on quora
The Nazi swastika's resemblance to Hindu symbol is no accident. The Nazis had substantially twisted Hindu ideals to suit their needs. The word "Aryan" that Nazis were so fond of is from the Sanskrit word "Arya" meaning supreme, pure -- to denote a class of people. While in Hindu sense it is used in more positive contexts (suave, refined, scholarly), for the Nazis the word meant the supreme race.
Heinrich Himmler, the dreaded head of the SS, called himself a Kshatriya (the second highest caste), performed yoga exercises and carried the Bhagvat Gita. He was delusional in assuming himself as the Arjuna (the hero of Mahabharata). He assumed that he was leading a just war. See: Nazi leader Heinrich Himmler a fan of yoga - Telegraph
One of the key thought leaders in the Nazi group -- Savitri Devi (actually a French woman with the original name Maximiani Portas) -- claimed Hitler to be an avatar of Hindu god Vishnu. According to Hindu mythology the last avatar of Vishnu -- Kalki -- would destroy the world and take the good people to start a new cycle. For the Nazis, Hitler was the Kalki. As Savitri Devi thought herself as a thinker, she called herself a Brahmin (top caste in Hindu system) and married one. It was she who connected the India's rebel leader Netaji Bose to the Axis powers (especially Japan). (For his part, Bose married an Austrian - Emilie Schenkl and the couple was treated very well by the Germans.)
Hindus were/are not interested in any of these crazy comparisons of Nazi leaders with Hindu gods and for the most part unaware of what Hitler did after he wrote his autobiography. There are no holocaust deniers, however some fringe Hindu groups are still fond of Hitler & his boys (Hitler's "Mein Kampf" was always among the best sellers in the bookshops), while also believing Israel is the ultimate model for India & Jews as the model for Hindus. Oh, the irony!
Balaji's answer-Quora
Edited by Fermion, 19 November 2017 - 07:15 AM.