No, they are different things with the same name. That's why it shows as installed. But the PlayStore update will never work because the signature is different. Once you switch to Obtainium, you have to keep using it or uninstall and try another method. 

 Got it! I was concerned about installing apps outside the Playstore, and if there was an update through the Playstore, my phone might force the update through the native store. Thank you! 

 Well it's not obvious. I only started noticing this once I developed my first apps. And somehow google play could update my manually downloaded test APKs as soon as my app got released.

The magic is in the signing key :) 

 Oh I see! Didn't realize they used different signing keys.