看一下对三个词的英文解释：
An index manages user accounts, permissions, search, tagging, and all that nice stuff that’s in the public web interface.
A registry stores and serves up the actual image assets, and it delegates authentication to the index. Docker registry is a service that is storing your docker images.
Docker repository is a collection of different docker images with same name, that have different tags.
Index是管理docker的服务（包含用户账户，操作权限，等等）。Registry是存储docker image的服务。Repository则是包含同名不同tag的docker image的集合。
参考资料：
Difference between Docker registry and repository；
Where are Docker images stored?。