I wonder if this is a case of specifying something (closed cell) to be sure to get some particular properties that you've seen in closed cell foam, though either type of foam might be available having the desired properties.

If you describe what you want the packing material's properties to be, maybe a person who knows foam can tell you of something cheaper or better than closed-cell foam at meeting your needs.

That's what I'd do, but then I'm not a foam or other packing material expert.

By the way, styrofoam, if you could call it a foam, has closed cells.

And no matter what you do, if you use small pieces such as styrofoam peanuts, stuff inside can slosh around. If you have something heavy, you need solid surfaces and shapes to hold it in place in the carton, which is exactly why formed styrofoam is used on so much stuff.