Yes it is heavy cream and whipping cream the same. Half and Half is part heavy and milk. Usually used in making ice cream.
There is a difference between heavy whipping cream and whipping cream. Heavy whipping cream has a higher fat content and will whip to a slightly thicker product.
In many things they can be interchanged with no problem. If the whipped cream product is an important part of the recipe, heavy whipping cream is a better choice.
Whipping cream has about 34% fat, Heavy cream has 38 to 40%. It is much more stable for mousses, fillings, etc.
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