Yes, Strongbox is now a universal App, which means it runs on both iOS and macOS, and uses a single license across these platforms.
The license is linked to your Apple ID. So no matter what device you use (iPhone/iPad/Mac), as long as you are signed in with the correct Apple ID, you will have access to Strongbox Pro.
NB: You may need to tap the ‘Restore Purchases’ or 'Already Purchased' button on the Upgrade screen.
Is there any difference on macOS between the new Universal Apps and the previous macOS Apps?
Zero. Absolutely None. Both apps will remain identical feature wise forever. They will receive updates and features on the same schedule forever. No difference. Apple unfortunately provides no way for us to merge the Apps so we have to support both, which we will continue to do.