Whipping cream vs. heavy whipping cream?

Yes, either will work just fine. Perhaps this will clear a few things up:

The term "whipping" simply indicates there is sufficient fat for whipping, nothing else.

In the U.S.:

Half-and-Half runs about 12%

Light Cream is regulated to 18-30% fat but runs around 20%

Whipping cream / Light Whipping Cream is 30-36% fat (you need at least 30% for whipping, to at least double the cream's volume). Runs about 32%

Heavy Cream / Heavy Whipping Cream 36+%

Manufacturer's cream about 40% (a foodservice product and "Yum!")

Note: The heavier the cream, the better it will whip and the more stable it will be. Ultrapasteurized cream has a longer shelf life but reduced whipping capacity. Any of these products may or may not have emulsifiers and stabilizers added and may or may not be homogenized.

Where I live whipping cream is around 35% fat. Heavy cream is about 35% fat.
Perhaps the confusion is due to what country the recipe is written and which term is most common there.

Either should work just fine. I think heavy whipping cream may have slightly more fat--you can check the labels. I actually usually opt for plain ol' heavy cream.

So I just happened across the 'heavy cream in ice cream' post. Of course it didn't come up when I searched the database lol. But I'm still not quite sure which my recipe wants... It's a really simple one for making caramels (not sauce).