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tagdocker image的集合。

参考资料:
Difference between Docker registry and repository
Where are Docker images stored?