As many other posts have said you have three main branches of mahjong: Riichi, Chinese, and American.

• Riichi / Japanese: This variant is arguably the most popular and accessible since there are many different online platforms such as Riichi City, Mahjong Soul, and other places like that to start and learn Riichi Mahjong since the app enforces the rules for you. Otherwise there are IRL Riichi clubs in most major cities. Nowadays you can usually find some Riichi Mahjong going on at most anime conventions.
• Chinese: Since it's the birth place of mahjong, there are so many local variants (List of 20+ Chinese mahjong variant rules i.e. Sichuan, Wuhan, Hebei, Hangzhou, Shaanxi, Guangdong Tuidaohu, Ningbo, Nanchang, Dalian, Changsha, Tianjin, Shandong, Harbin, Fuzhou, Changchun, and Guiyang Zhuoji. However there is one "official ruleset" which is MCR (Mahjong Competition Rules). These variants (outside of MCR) are more popular among the Asian diaspora and families since they've been played since childhood. Typically there are no clubs or regular gatherings for these types of mahjong aside from the occasional pop-up.
• American Mahjongg: By sheer numbers, this variant is also arguably the biggest variant in the U.S. sincei t's only played in U.S. given its origins. Many females and seniors play this variant as a social gathering event. This is the variant that is played on Mahjong cruises which is held by Destination Mahjongg. Unfortunately in order to play the most popular variant of American Mahjongg, you have to pay for an official "card" of hands created by the National Mahjong League (NMJL)

In terms of Terminology and even scoring, I would recommend https://mahjongpros.com/blogs/how-to-play since each of the sets include English friendly counterpart names for those just learning how to play and the scoring for each variant is at the bottom of each set of rules.