Let me take it a step further....
Let's say I own a grocery store and it's called "Tender Rebel Groceries". I have made a great name for myself locally. Now a vacant lot across the street has opened up and someone buys it. Low and behold they put a grocery store there as well. Completely fair and they have every right to challenge me to become the new Grocery King but one day I come into my store and notice their new sign out front and they have named their store "TenderRebel Groceries". Should I just let them market themselves on the success I built on my name? Or should I file a lawsuit for them trying to piggy back off my success???
You bet your butt I am going to file a lawsuit. They have every single right in the world to be a grocery store but they have no right to infringe on my successful brand name.
To me it's more like naming something "quik-e-mart, quickie mart, quicky mart" now they are all spelled different, yet they sound the same. As people have pointed out in other places, app is a description of what they sell in their store, short for application, it's just too broad of a name/description. So if i spell it @ppSt0re or appstor does it get the same rights, if definitely should not. This lawsuit will not go anywhere until the one with microsoft and apple gets finished, to even see if the courts uphold "app store" as a real trademark or if the government overstepped it's boundaries on this one. Now i will say to people that think this is dumb, that there is no police to keep people in line from stealing a name or using it without authorization, and if this does somehow constitute an infringement, and apple looks the other way, then they are basically condoning the violation of it. So for that, i can completely understand why they are doing it, but i don't think it will go anywhere.
I guess my only question is, would it even be called an App Store if Apple hadn't started that? And this is a legitimate question, not meant to be sarcastic, b/c I wasn't around the mobile world much before the iPhone, so I really don't know... but if it wasn't for Apple, isn't it possible it could've been called, generically speaking, something like "mobile program store" or "program market" or "mini-software store" or something else generic like that? Would they even be known as "apps" if it wasn't for Apple starting that? I get that they are applications, but I don't remember growing up saying "hey I need to go home and install this application on my Dos 5.0 machine".