The Japanese term for the outdoor food carts that helped popularize tempura around Tokyo Bay is yatai. A yatai is a small mobile food stall, traditionally arranged as a pushcart or compact street stand.
During the early 17th century, food-stall culture expanded around the Tokyo Bay area. Vendors used fresh seafood and a lighter, minimally mixed batter, helping create the Tokyo- or Edo-style tempura associated with modern Japanese cooking. Because tempura was cooked and sold outdoors, customers could eat it immediately, often with dipping sauce and grated daikon.
Yatai is broader than tempura: the word describes the food-cart format, not one particular dish. Depending on place and period, yatai have sold soba, ramen, gyoza, beer, and other foods. “Izakaya” means a drinking-oriented eating establishment, “ryokan” means a Japanese inn, and “kura” commonly refers to a storehouse or warehouse, so none of those terms identifies the carts in this question.