When you're checking on your downloads and see there's a difference in the number of downloads there are a few reasons why this might be.
Google Play listings show a range of downloads only eg. 10+ installs, 100+ installs, 300+ installs etc.
Your application may have been published to other locations where users are downloading it from. While Nobex Partners only publishes your application to Google Play, occasionally other distribution services will make the .APK file available for download. This installs are tracked in your Partner Dashboard, but not in your Google Play listing. You can see if your app is published anywhere else by grabbing the package ID from the Google Play listing URL and searching Google for it.
Note: in this example there were 6 pages of results.
While users installing the app from sources outside of Google Play will not necessarily affect the app's performance and will still contribute to your station's ad revenues, it is a potential risk for your listeners because the files are not guaranteed to be safe and there is no path for updating outside of Google Play.
It is best to make the link to download the app from Google Play as easy to find as possible. You can set up a widget on your website with the direct store links. Just visit the Website Widgets tab in your Partner Dashboard.