The question is:
LuckGrib is available on both iOS and macOS, and the application has the same name on each platform. If I was to buy the app on iOS, would the purchase transfer to macOS? (Or the other way around?)
The short answer is: no. If you want to run LuckGrib on macOS and iOS, you need to purchase the application on each platform.
Although the app has the same name on iOS and macOS, they are completely separate applications.
The two apps are similar in many ways, but they also have many differences. Everybody seems to agree that the iOS app is easier to use, and it also comes with some built in tutorials, which can be useful.
The macOS app has more features, which may or may not be useful for you, depending on how you use the application. For example, meteorologists using the macOS app have the ability to extensively customize the draw styles. If you are happy with the parameters currently supported in the application, you may not need this ability. Sailors may also prefer the macOS app as it offers more help with weather routing - however, again, if you don’t need this ability then this may not matter. Weather researchers may enjoy the ability to import huge files on macOS, as Mac’s can be loaded with lots and lots of memory.
There is a considerable effort needed to implement and maintain each application. The author does not cut corners in the app development - a great deal of care and attention to detail is exercised in the development of both of these applications.
On a more technnical note regarding sharing a purchase between iOS and macOS - this isn’t currently possible in the Apple App stores. Apple has no method for sharing in-app purchases between iOS and macOS. This is true even if you share the same AppleID on both platforms.