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When the docs say “data”, it’s talking about fixtures. Simply, you need to update any datetime strings in your fixtures when moving to a database that is TZ aware. So, the section futher down referring to fixtures contains the additional info you’re looking for.
That said, this is not something that you should be changing back and forth between development and production. A lot of people like to use SQLite for development (for good reason), but it’s unfortunately not currently TZ aware. So, if you need to create a site that is, you really need to use a different database in development. TZ aware data is tricky and this is not something you should be testing for the first time once you go to production. You should be dealing with it as you develop, so you know it will work in production.
As a result, Django’s advice is focused on one-time migration of old TZ naive data to TZ aware data, not how you can switch them back and forth on a whim.