Federico Sasso: Google officially never used the two terms, as far as I know.
The "sandbox" actually didn't really exist: it was a mental model used by SEOers to explain sudden changes in ranking. Adjustments in positioning were at the time an expensive operation performed in batch sometimes every while and then; after the release of the Caffeine update - where such adjustments happen continually - such phenomena disappeared.
I heard the term "penalty box" to describe the state of a site manually penalized, when it actually disappears from SERPs until the penalty is lifted.
Edwin Jonk: As far as I know a "sandbox" is a state where a site sits at (lets say) page 3 and doesn't move no matter how many links you build to it [1]. The term is never used by Google and it is mainly discussed by black hat SEO's. The term dates back to 2004 [2].
What is the difference between Google Sandbox and Google Penalize Box? 
