I think Google's doing themselves a disservice by trying to make the Chrome Web Store sound too much like the App Store. It sets up the wrong expectation.

There's already a user backlash visible in reviews. A lot of people are disappointed that a Gmail app is just a link to the Gmail website, for example.

Here's a quick vocabulary of Google's terms and what they actually mean:

app – website

store – directory

install an app – add a bookmark

paid app – paywall managed by Google

in-app purchase – paywall managed by third party