Handbook 2: 9.4.2 outlines and describes Additional Relief Society Meetings. They are usually held monthly but may be less frequent. They are planned under the direction of the Relief Society presidency and at least one member of the presidency attends them. They are official Relief Society meetings.
Additional Relief Society Meetings replaced the former monthly Homemaking Meeting. They allow more flexibility for the Relief Society presidency to meet the needs of the sisters.
Although all of the sisters in the Relief Society are invited to attend, the meetings are not mandatory, and it is not expected that all sisters will be there. Varying subjects and activities will be of varying interest to different sisters. But they are a formal part of the Relief Society program.
Now, if Liz wants to start a book club, she does it. She invites people she knows, and she invites as many as she wishes. And while many of them will happen to be Relief Society sisters because on her circle of friends and influence, her book club is not an Additional Relief Society Meeting and is not an official part of the Relief Society. In our area we have book groups, quilting groups, and lots of other groups created by sisters for sisters and friends with similar interests.