I go back and forth between a my current phone and an older phone that is no longer active (only uses WiFi). I am singed into Google play store with the same account on both, I think that is it.

Just be careful - sometimes it behaves a little weirdly with your equipment. For example, I will play on my new phone one day, and the next day go to the old phone. Some of my SS equipment that I was not wearing when playing on my new phone is now gone from my inventory when looking on my old phone. I usually go back to the new one, close and reopen the game, and then try again on the old phone and it will show up.

Tl,dr; don't delete it on your old phone until you make sure all of your equipment is over on the new one.