I was quite surprised to find out that this is not only false, but it is defined by US Government regulations. Whipping cream must contain at least 30% butterfat but no more than 36%. In contrast, heavy cream must contain at least 36% butterfat. What does this mean to you, the cook?
When making whipped cream, heavy cream takes longer to whip but lasts longer once prepared (before losing its peaks and becoming watery). In contrast, whipping cream whips faster but does not last as long. Both kinds can be used for cooking.
You will sometimes see light cream, and this contains 18-30% butterfat. It is not suitable for whipping.
A more important difference exists between creams that are pasteurized vs. those that are ultra-pasteurized. Both treatments kill bacteria and extend the shelf life of the cream, but the ultra procedure uses a much higher temperature. The result is cream that lasts longer (in the unopened container) but does not whip as well or taste as good. Look for local, pasteurized (not ultra-pasteurized) heavy cream that is free of additives.