I was confused trying to figure out how they would interoperate, or be useful in the same project. Turns out the desktop version is in C++ and the mobile version is in ActionScript. I assume there were good reasons for this.

The names are kind of misleading, as there appear to be both iOS and android ports of the "desktop version". I'm not sure which version you actually get if you buy the game on iOS/Android.

The original desktop release in 2010 was based on flash (presumably using Adobe Air for desktop? There was also a flash web demo), but there were issues, and flash was really hard to port to linux. So they rewrote the entire game in c++ in 2011, for easier porting. It's that rewrite that is what's labeled as "desktop version". It's the most up-to-date and polished version.

The "mobile version" is a fork of the original 1.0 flash code base, and IMO it's only really interesting because it's much closer to what Terry originally wrote.