I know it is not the same as evaporated milk. Not even close. As for the difference between heavy cream and heavy whipping cream, I'm pretty sure there isn't one but maybe others will have a different take on it.
Heavy cream will only whip up if you want it to! I'd say you can use them interchangeably for whatever the recipe calls for. Just don't use evaporated milk.
What kind of ice cream are you making? Can I lick the beaters?!?