Use of ionic as desktop web application
Ionic is a great framework to develop mobile apps using html5. We want same application to be used over desktop browser also. Will it be good idea to make a single responsive UI that works best on both desktop browser and mobile browser and make app. OR we should make different development for browser and mobile app.
Answer
To expand a little bit on what has already been said, Ionic is is built and tested for mobile only. Internet Explorer for example is not tested and does not properly handle a number of the features in Ionic. Desktop browsers do have different features from their mobile browser counterparts. You would seriously limit the browsers that can use your application on a desktop.
Most likely, you should provide two different applications for desktop and mobile. Unless you have the guts or ability to tell your users that they must use Chrome (or Opera) to run your website, you'll want two separate applications. You could still use Ionic for a mobile website though, but without being able to use Cordova's full platform integration (you would be limited to the native HTML APIs provided by the browser). You could certainly retain much of your business logic in a common core that is shared between both applications. That would require creating a shared angular module(s). I have done this in a project with an Ionic app and a normal Angular desktop app (with Bootstrap).
There are a number of ways to detect if a visitor is coming from a desktop or mobile device. I don't know of a method that is 100% perfect, because they usually rely on the browser's user agent string (and can be spoofed, changed, etc). See http://detectmobilebrowsers.com/ for some common scripts or examples how to implement mobile detection on a server or in a programming language.