Whining and Whinging amount to the same thing but they are two different words, that are pronounced differently.
Wining is wine-ing, as wining and dining. Whing-ing is winge-ing, as in binge drinking, or perhaps cringing, as an animal might do if you threatened it with a good smack.
When a child has been refused sweets ( your candy ! ) they might whine a bit but if they continued being annoying, than they would be described as whinging.
Interestingly, my spell checker isn't having whinging one little bit, and it is set to English English, not American English !
I think whinging is a type of word that has a special name, probably PORTMANTEAU. Here is the Blessed Wiki on the subject ::
http://en.wikipedia.org/wiki/Portmanteau#Standard_English
Sorry if this is perhaps too much information !
Please feel free to ask us brainy people here on AB if there is anything else that us Brits say or do that puzzles you....we are only too glad to help !