I think it's safe to say that American English prefers "practice" in all situations.

Beyond that, all I can do is refer you to your favorite dictionary. http://www.dictionary.com/ will give you information from several all at once. Most of them indicate that "practice" and "practise" are spelling variations of the same word, that they are equivalent in meaning, and that "practise" is used chiefly by the Brits.

On the other hand, the dictionary that Andy Neil recommends, at http://dictionary.cambridge.org/, makes a distinction in meaning between the two, as you thought.

The database for Firefox's spell checker was apparently loaded by Yankees.

-- Russ