The short article shows you how to resolve the error “A different version of this App is already installed with the same version number. You need to delete the app from the site and the site recycle bin to install this version.”
You developed your App for SharePoint half way then the above error appear. But you have Removed the App and Delete from Recycle Bin. So??
You need to go to your AppManifest.xml in you SharePoint solution.
Change the Version number, any number will do but normally I change the last one.