Call it a chemisette and a dickie. Both are used and are good search terms. Not only were they popular in the 30s and 40s, they were also worn under jackets and certain V-front dresses in the Edwardian era, teens, and 20s. AND... there are even some from the mid-19th century, too. They've been around for ages. This one looks to be from the early-to-mid 1900s.