Except, therein lies the rub. Because, contrary to what you may believe if you've ever perused the games available on the App Store, you're not allowed to make demo versions. Apple don't allow them. Submit one, apparently, and you'll find it thrown back in your face. Upon discovering this I was initially confused but, as it turned out, it actually solved for me a lot of problems.
You see, up until this point I'd been wondering not only which bits of the game to give away for free in the demo version (which I wasn't going to be allowed to make) but how the demo version (which I wasn't going to be allowed to make) and the full version should overlap. The full game features a variety of unlockable goodies, 10 of which are power-ups. I'd decided to put three of these into the demo. So what if you play the demo for a while, like it and buy the full game? Should the power-ups you've purchased carry over? Should the high score table be shared? Should your achievements (or 'accolades' as they're known in the game, but I figured I should use more commonly accepted terminology here in order to clarify things) carry over? And if so, how? Would this mean I'd need to completely rethink the underlying file handling code I'd written, in order to access the same data from multiple apps?
Then I read Apple's "no demos" rule. And suddenly, all those problems went away.
Apps aren't allowed to have unfinished or permanently locked functionality. They can't have menu options which never become available, or say one thing (such as "Play Challenge Mode") and do another (such as just pop up a message box or take you to the App Store page about the full version). They have to be complete products in their own right.
And it makes a lot of sense. A lot of products on, say, Xbox Live Arcade have menu options or in-game prompts for actions like MULTIPLAYER and NEXT LEVEL and CUSTOMISE YOUR WEAPONS yet when you select those options you're just taken to a screen explaining how you can't do that in the demo. I can imagine why Apple decided they didn't want their devices full of products with similar dead ends. Anything which takes you to information on buying the full version of a cut-down free game has to be marked "Unlock More Levels" or "Buy Full Version" or similar. And that way, folks who are actually happy with the free version of a game (and there will certainly be a lot more people that fall into this category than will actually buy a full version no matter the price) shouldn't ever stumble accidentally into a "You can't do that in the free version!" screen... because the only things which look available in the menu system or the game itself are things which are actually available.
Hence Ballpit Lite having its own high score tables. Hence it going straight into the game when you select "Play" instead of into a submenu where you pick a game mode. Hence the power-ups not carrying over into the full game (and, it should be mentioned, nobody's complained about this - it doesn't take long to unlock them again in the full game anyway). Hence the power-up unlock screen only listing the three things which are available in Ballpit Lite, rather than listing all 10 power-ups and the other unlockable goodies and permanently greying most of them out.
Above all, it's meant that I can actually put stuff into Ballpit Lite which isn't in the full game. The game mode playable in Ballpit Lite has a time limit - this game mode doesn't exist in the full version. Version 1.2 of Ballpit Lite (not yet released, at time of writing) will feature achievements for the first time... but they're 8 completely different achievements than the ones in Ballpit, rather than being a subset, so I don't have to worry about whether (or, indeed, how) people who have collected 90,000 points in Ballpit Lite should start off 90% of the way through the scoring 100,000 points achievement if they start playing Ballpit. They are, for all intents and purposes, completely different products that just happen to have been made by me, have similar names and feature a certain amount of overlap in the gameplay they contain. (In fact, I've actually suggested to some people who've bought the full version to download Ballpit Lite too, as it contains a game mode not featured in the version they own.)
Which only leaves one question to be answered: why in the world does everyone who makes a free, cut-down version of their latest game - me included - insist on spelling Lite like that?