…in terms of being used as a baking ingredient
"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.
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.