Heavy cream or heavy whipping cream and half-and-half are not the same. They are dairy products that differ in butterfat content and they are used for different things, according to The Joy of Baking.
Heavy Cream
Heavy whipping cream has a butterfat content that ranges from about 36 to 40 percent. Whipping will double its volume. It will hold its form well and can be piped for pastry decoration, unlike light whipping cream.
Half-and-Half
Half-and-half consists of cream and whole milk. It has a lower butterfat content that ranges from about 10 to 18 percent. Since it cannot be whipped, it is used in liquid form. Half-and-half is often added to coffee, tea, or other beverages.
Whipping
To whip cream refers to beating it in a circular motion with a whisk or electric mixer. Whipping makes cream fluffy by incorporating air into it. Whipped cream has a rich taste and often accompanies desserts as a topping or filling.