To whinge implies to complain, usually about a specific circumstance, with the intent of causing something or someone to change because of your actions. To whine suggests making annoying complaints for the sake of complaining.
I agree with the good doc, but would add that whinging* is usually about trivial matters and often with no real expectation of change though the possibility is there - "Mum, why does my brother ALWAYS get the window seat?" - "Oh, stop whinging!".
It is usually only small kids (or adults behaving like them) that whine as doc says in a continous stream "I'm cold, aren't we there yet? How much longer are we shopping? I don't like this sweet, I want that sweet".
And dogs whine not whinge.

* or whingeing, to cross threads.