Synaptic 'initialize', 'initialise' - why the difference?

Theoretically, there should be separate spellings depending on your system's locale settings. If it's set to Australia, you should get "initialise", while you should get "initialize" if your system is set to the United States.

That said, English varieties sometimes get a bit mixed up, so you might not actually see what I've described above. If so, it's a bug, so you should report it.