It's just that I saw the BBC use it on their News 24 channel, and that really threw me off. I checked in my OED, and it states that a 'kidnap' is 'an instance of kidnapping'. What's that supposed to mean? It does not list 'kidnapping' as a noun, but rather, the present participle of 'kidnap'.
The entry in the OED suggests that "kidnapping" is the general word for this crime/activity, such as in "Kidnapping occurs a lot in Cambridge".
Then when it happens (i.e. there is an instance of kidnapping) it's a kidnap. I can see the difference between the general noun and the specific one, but like you I don't see the difference between a kidnap and a kidnapping.
I think it's a fine line between the two. I would say (though I could be wrong) that you can't go wrong by using "kidnapping" because I can't think of an example where "kidnap" would be used over "kidnapping".
I don't see any difference either, and I haven't heard kidnap used as a noun until I read this thread. Since kidnap is listed in the dictionary as a noun, and the using the gerund is a common way to convert many verbs into nouns, both ways seem to be correct.