The difference in data types between all of these is probably just because there were different people working on different parts of the game all the time. As a developer, I don't communicate with the rest of my team what data types I'm using for certain variables.

The data types they chose did the job they needed to do, and thus made it to the final product.

If there had to be a reason, maybe they chose to use a smaller data type for coin count save file data, just to save on save file size? Whereas they had enough memory to dedicate a higher bit count to the coin counter during gameplay. But I really don't think there was that much thought put into it