In the strictest sense, a web-app is an app that runs "in any browser", accessible through a URL; a native app one that runs "in a specific operating system".

In the strictest sense, a web-app is an app that runs "in any browser", accessible through a URL; a native app one that runs "in a specific operating system". Requiring Internet access or not has nothing to do with it. For example, an OS X native app wouldn't run in Linux (at least as easily as a Linux native app would). A web app would.