Yes I am saying that an OpenSim installation that doesn't have "registered" users is not a grid. It doesn't have to be an "open to everyone" public registration. Schools would only allow their staff and students for instance.
Your Hyperica, in my opinion, is NOT a grid. It's like what? 4 regions that have hypergrid portals in it? At the most it is a transfer station to actual "grids" and to other peoples standalones. It's your personal standalone that you open to the public to come and visit. Like a home. You can invite people to dinner but that doesn't make your home a restaurant.
But if you are going to call every standalone that has an hypergrid gate on it a grid then I guess you should call real grids "Virtual Worlds". I'd be OK with that. Or maybe call the small ones mini-grids or pocket grids or sub-grids or something like that.
My point is there needs to be some sort of distinction. To me that distinction is the ones that house the database/asset server or whatever for the residents and have an actual registered users.
All I know for sure is that I really hated being called a Grid when I had my nine regions up with an HG gate. It wasn't true. And it caused me problems with people thinking that.