Even though I think many may find this question stupid, nevertheless I wanted to understand it. Also, are Google apps the one made using the Google App engine while the Chrome Web Store apps made using the Google Web Kit (GWT)? Is there any difference between the these two types of apps as far as the end user is concerned ? If not then why does Google need to have them hosted on separate urls?
Google Apps: A suite of applications that are created, run and hosted by Google, which can be used by organizations / educational institutions. These include Gmail, Docs, Calendar, Contacts, Chat and some other stuff. Also gives you a Google id of the form email@example.com. All apps are also hosted on your own domain.
Google App Engine: A platform that Google provides on which you can write your own application, in either Python or Java. You write the app and upload it to Google, and they run it on their servers. They also expose some APIs which you can use for things like data storage, chat, email, images, authentication, etc.
You can use Google Apps to provide mail, docs, chat services to your business. You can write any custom applications you want and host it on App Engine, or somewhere else. You could add the application you wrote to the Chrome Web Store if you want to. Finally, you could write the client side code for your app in Java if you want to, and compile it using GWT.
Does that help?
I wouldn't say that
[all] these apps [listed on chrome web store] are for Google Chrome browser.
Indeed, it's true for Chrome extensions only. But many applications listed on Chrome webstore also work fine with other browsers like Microsoft IE. The applications end up listed when you click the "Applications" button on Chrome (or type in 'chrome://apps' in the URL input). But this is merely a shortcut.
However many Chrome WebStore applications go along with Chrome extensions, though it's not mandatory. Also Google provides development kits and APIs but you can use other developement tools.
First of all no question is silly.
Second what Sudhir said is exactly right, I will try to give you simplified version of that.
Google Apps is suit of application like Microsoft office but on internet.
Google App engine is a platform for developers to write application against it.
Chrome web store is like apps on iPhone but unlike phone these apps are for Google Chrome browser.
All these apps are pretty much written in Java so end use should not have any issue with this.