No, hard water and ice are not the same thing.

We have hard water. Blast. It sure makes cleaning tough, and it makes our brand new dishwasher look like a chump. Rinse aid does squat.
I have yet to find a great cleaning product that takes away the calcium deposits (aside from CLR, cause I gotta do counters and the like) for surfaces foods and face products will come in contact with. But, I have found that soaking my utensils in a bit of water and vinegar takes the white gunge away! Hooray! I was afraid the white film would be permanent. I have also learned that there is a product called "Lemon Shine" that'll help with the dishwasher.

Oh, yes, we do have a water softener... its just not hooked up right now. Soon.