The difference between heavy cream and whipping cream is mainly in the fat content.
Heavy cream contains more fat than whipping cream, which means sturdier whipped results and whipping cream contains less fat, which results in a fluffier and softer topping that does not hold as long as heavy cream.
Heavy cream or heavy whipping cream contains 36% or more fat content than whipping cream and heavy cream is also thicker and richer and whips to stiff and stable peaks that hold it's shape well.
Heavy cream or heavy whipping cream is best for stabilized whipped cream, and for rich sauces like Alfredo sauce, soups, custards, ice cream and ganache.
Whipping cream also known as light whipping cream contains around 30% of fat content although some whipping cream can contain up to 36% fat content.
Whipping cream or light whipping cream is also softer and lighter and whips to soft, pillowy peaks which are less stable and deflate faster.
Whipping cream or light whipping cream is best for a quick dollop on cakes, pies, or hot chocolate where you want a lighter texture.
You can sometimes substitute heavy cream for whipping cream although the results can differ slightly.
You should use heavy cream when you require structure and use whipping cream for a softer, airier finish.
You can use heavy cream instead of heavy whipping cream (and vice versa) for almost any recipe because they are essentially the same product, both containing at least 36% milk fat and being used interchangeably in the U.S. for richness in sauces, soups, and desserts, though the slightly lower fat in "light whipping cream" yields a softer topping.