SharePoint access control lists vs. "Invite people"

Hi everyone.  I'm getting myself in a bit of a pickle over access controls on a SharePoint site which is part of a Group.  When a Group is setup, the usual Owner, Members and Visitors SharePoint access control lists are added automatically to the SharePoint site.  However, when you invite people to the Group / SharePoint iste, they don't get added to these lists, they stay empty.

When I want to expand access to the information in SharePoint, should I be adding people to the Vistors / Members lists or just inviting them to the Group and saying whether they can read or edit???

I've done loads of searching online, but can't find any articles or support information which clarify my confusion.

Thanks for your help as always, Oz