I see a lot of hypocritical MSFT fanboys on here. You attack Apple for "app" but ignore windows, office, word, excel, access, outlook, exchange, visual, studio and expression.
The "Mac App Store" and "App Store" are not generic because they are the online software stores that sells "apps" with an app file extension.
MSFT is free to create an "EXE store" or an "Program Store" as those are terms which they use in their OS documentation and literature.
From early on, Apple has used the term "application" or "app" to refer to programs and these programs were bundled inside an application package called a fat binary which had not only the executable code but also resources. With the advent of OS X, applications were provided in application bundles with the extension of ".app". If you choose to display extensions, you will see that all applications in the /Applications/ folder have a ".app" extension.
Applications on iOS devices also have .app extension but you just never see it unless if you jailbreak the device and use a file manager.