Apple is trying everything to defend its App Store trademark. However, it looks like the company is about to lose its bid in Court against Amazon, as the judge announced that Apple had not proved yet the risk of confusion for consumers because of the use of the name App Store by Amazon (it seems absolutely evident to us). In the mean time, Amazon is resisting and still refuses to change the name of its online store. Microsoft is also taking part in the procedure to invalidate the trademark as it would like to use it as well.


On the other side, Apple keeps sending legal threats to whoever uses the name App Store. The last one that received one is a small company called Amahi.


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Other companies got similar letters as they were using the name App Store. As a reminder, these letters are sent by law firms mandated by Apple, which get paid for every mission they complete, so it is not surprising to see that many letters going out to every single company using the name App Store.
By Machmeter, original by Lionel

Which seems absolutely evident? That there is confusion or that there is not confusion?

If you say there is confusion could you please show any instances where someone thought Amazon's app store (the name is not "App Store by Amazon," by the way, it is "Amazom.com Appstore for Android") sold Apps for iPhones, etc.

Sorry indeed there can be some confusion on whether there is confusion
There is no confusion, nobody would think that the Amazon Store (which is as you said for Android) actually sells apps for iOS. that's the problem for Apple here, they chose a name that is too simple and yet their system is so closed that there can be no confusion with the other online stores.

What really irritate me is, how picky apple is with anyone who try to "steel" their intellectual property in any way, but they (apple) have no problem to call a device iPhone, a service iCloud although they do not have legal right to do that, because some other company already own it.

Apple has a long history of doing this, from the very start when they called themselves Apple and got into a row with Apple Corps. I believe they had a similar problem with McIntosh (makers of high-end audio equipment.) Besides using names they haven't secured rights to, they copy, wholesale, other developers' ideas... for instance Dashboard / Konfabulator or Sherlock / Watson. And in advertising when they basically recreated a The Postal Service video to announce the switch to Intel. The boot-up video on earlier AppleTVs was a recreation of an independent artists's video. The original iPod (now the iPod classic) menuing system is a direct copy of Creative Labs's players from 2 years before the first (Mac only) iPod hit the market. Apple even went after an Australian grocery store chain, Woolworths, for their logo which is an apple peel shaped in to a W (intact, no bite has been taken out.)

I didn't have to Google for any of these examples, they are all things that pretty much instantly came to my mind. Just imagine how many more instances there are that I can't recall.

But do let me say, I adore my Mac and I cannot see myself using any other computer. However, Apple as a company... I can't stand them.

I mentioned this two cases because they are fresh in my mind but there is a lot of other examples as you pointed out.
Let me say it this way - I love my Mac, but unfortunately after almost 15 years of using Macs, I couldn't say the same about apple.