…in terms of being used as a baking ingredient
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Merrill is a co-founder of Food52.
"Heavy cream" and "heavy whipping cream" are the same -- they contain 36-40% butterfat. Plain "whipping cream," however, has only 30% butterfat and doesn't whip as well as heavy cream.
While Peter no longer works for Food52 he still thinks up ways to make the website better.
To add a bit to Merrill's excellent answer, a lot of "whipping" creams have carrageenan added as a stabilizer. I have no idea if this affects any other use of the cream though.
Usually the same- depending where you live.