How do I translate the words “player” and “team” into Mandarin? I have noticed there is a large number of words that translate as “player” and “team”. I've been trying to decipher those and so far it seems that:


  玩家 wánjiā, 玩者 wánzhě  – those two mean a player of a game
  
  竞赛者 jìngsài zhě – this one would be a contestant in a game such as
  race?
  
  游戏者 yóuxì zhě – a video game player or gamer
  
  球员 qiúyuán – player of a game involving a ball, such as football,
  basketball (golf?) etc.


And there there are the teams:


  班 bān – team?
  
  团队 tuándu – team?
  
  组别 zǔbié – team?
  
  球队 qiúduì – sports team involving a ball


Is my thinking correct? What is the difference between those terms? Are there other terms I am missing here?
Your thinking is correct!
班 is always 班级 (bānjí) — usually it means "class"

团队 (tuánduì) — you might consider the word as "group"

组别 (zǔbié) — also means "group", but it doesn't always have many people in the group

球队 (qiúduì) — sports team involving a ball, it's only used in ball games, like 足球队 (football team), 篮球队 (basketball team)…