User groups and access levels are not the same thing

Groups decide what someone may do. Access levels decide what someone may see. You need both, and they are configured in different places.

Groups

Under Users, Groups sits a tree. The defaults are Public, Guest, Registered, Author, Editor, Publisher, Manager, Administrator and Super Users. Groups inherit from their parent, so a permission granted higher up flows down unless something below denies it.

The permissions themselves live in Global Configuration and in every component's options, per group. That is where you decide whether Editors may delete, or whether a custom group may touch one component and nothing else.

Access levels

Under Users, Access Levels sits a much shorter list: Public, Registered, Special, Super Users. An access level is a label you attach to a group or several groups, and then to content. An article at level Registered is visible to anyone in a group that the Registered level includes.

This is the part that trips people up. Setting an article to Registered does nothing unless the groups you mean are actually attached to that access level.

Custom groups, the useful bit

Most sites need one or two groups the defaults do not cover. A client who may edit articles but not install extensions. A board that may see one category and nothing else.

Make a new group under Registered, give it exactly the permissions it needs, and make a matching access level. Do not start from Manager and take permissions away; start from the bottom and add. Inheritance means the first approach leaks rights you did not intend to grant.

Checking your work

The permissions screen shows a calculated setting next to every rule, which tells you what the group actually ends up with after inheritance. Read that column rather than the dropdown you just changed. It is the only honest answer.