I guess it will depend on which country, because yes it will be far more commonly heard in England than in the U.S. Dinner is more of a formal affair, and supper is generally more informal or a lighter meal.

Hah! You've opened a can of worms here. <---idiom. In the United States, the usage of these words varies from region to region, group to group, and FAMILY TO FAMILY. The U.S. custom is to have three meals a day, in the morning, at mid-day, and in the evening. As a rough rule, "dinner" means the main meal, the biggest meal of the day, and unless you know the family's own custom, you do not know whether that will be at mid-day or in the evening. "Lunch" always means mid-day. "Supper" always means evening. If someone asks you over for "supper" you do not know whether they call it "supper" because it is a light meal, or whether they simply called it "supper" because it is a light meal. Growing up, my own family had "breakfast, lunch, and supper." Supper was a big meal. On holidays like Christmas and Thanksgiving, the extended family would get together and have a gigantic meal, which was called "Christmas dinner" or "Thanksgiving dinner" which was usually in the mid-afternoon.

I use both words interchangeably in my home. The usage varies in different parts of the U.S. -- right now I live in Massachusetts, but I grew up in Pennsylvania. Even though it's only 500 miles apart, the vocabulary can be very different. Some Americans say "dinner" is a midday meal and "supper" is an evening meal. Some Americans, like Andrew (although he's not from the U.S.), feel that "dinner" is formal and "supper" is casual. You might have supper at home and dinner in a restaurant. Short answer, I think both are correct and either one ought to be understood by any English speaker. I hope that's helpful!

P.S. I don't think the word "supper" is outdated in the United States. But I myself might well be outdated.