They both do the same thing. They both create an endothermic reaction (which sucks up heat and makes the surroundings cooler) by melting ice.

For streets, we don't care if they're cold as long as they don't have solid ice/snow on them. So melting accomplishes this.

For ice cream, we want the ice cream to become cold, so adding ice+salt outside accomplishes this by melting the ice and making the ice cream container cooler.