What is enamelware?
Enamelware refers to metal kitchenware products coated in enamel — a process that's been used to make jewelry since antiquity. The Washington Post recently described enamel cookware as the "poor man's ceramic," and there's truth to that — the most popular color of vintage enamelware is white, because it was meant to resemble more expensive ceramic.
Beginning in the mid-19th century, enamelware became a staple of especially European homes, in part because the smooth, enameled surface made clean-up faster. Nearly any kitchen staple might be enameled: bowls, plates, pots, pans, teapots, coffeepots, kitchen utensils, and more.
What is graniteware?
It's basically the same thing as — or a subdivision of — enamelware. Graniteware is also produced by applying liquid glass powder to metal surfaces. "Graniteware" was used as a brand name by American producers of enamelware from the mid-19th century until the middle of the 20th century. I personally consider graniteware pieces to be brighter, newer, and lighter than European enamelware — also more functional (chunkier, rounder) and less stylish. Also, I frequently see graniteware pitchers and pans, but rarely see coffee pots or spice containers.