The Teppanyaki is a sit-down restaurant where the chefs cook right in front of you on a flat grill. It's quite a show and a lot of fun for children. We have two of these types of restaurants in my town, and we often go for birthdays, holidays, and with visitors. You sit with other diners around the grill and are served at the same time. (You may want to warn your children ahead of time, though, that the grill may flare up but that it's OK -- I've seen a few kids get scared by the fire)
The entrees consist of single or combinations of meat and seafood: shrimp, chicken, steak, lobster, etc., served with grilled veggies, rice and salad. They may have a child's menu, too. Check out the menu database on wdwinfo.com
The Yakitori House is counter service with skewered meats and other Japanese style foods. It's been a while since I've been there, but I remember thinking that it was one of the better fast food restaurants at WDW. It's not as fancy as the Teppanyaki, but is less expensive.
Both are good choices. There is also another restaurant in Japan that serves Tempura-style food. I haven't been there (yet!) but hear that it's good.
Hope you have a great trip!