Yes you are very right. The App Store is what Apple calls their way to put programs onto your iPhone. These programs however are not websites because you don't access them with your browser (like Safari or Chrome for example).

It's almost like there's two things here, and they do mostly the same thing, but someone... I don't know... "split" them.

Divided them, if you will. Made it so that there is a closed system of software that only users on certain "approved" hardware can access and use, and also locked those users into that system by preventing real competition.

I certainly am unable to see how that is entirely related to this conversation. It's a real puzzle to me...

I think you're not being serious, but I can see what you're trying to say. I don't think I agree because if you don't have an iPhone like my mum does, you can still do everything on internet. You can look up recipes and do all sorts of work. To her it's not really divided because everything already works. Apple hasn't done her any harm.