Keep iPad and iPhone apps separate
On your phone, navigate to Settings > iTunes and App Store and turn off the switch for automatic downloads for apps.  This will stop the auto download, but if you have purchased the app on one device you can still download it on the second device if you want to, it just won't happen automatically.

As is typically the case there are two lines of text following that section of the settings that read "Automatically download new purchases (including free) made on other devices."  So that is specifically what you are turning off.