While "shop" is often used (particularly for a woodworking class), a more formal term is industrial arts. Some high schools have an array of industrial arts courses available, such as woodworking, electricity, and small engine repair.
Home economics is having an identity crisis of sorts, sometimes getting a more modern name like family and consumer science. There's an interesting article about this transition that mentions:
Home ec has not disappeared, it's changed, evolving into classes focusing on child development, nutrition, family health, food service and hospitality. It hasn't been lost as much as translated. In 1994, the name of the course in most of the country was officially changed from Home Economics to Family and Consumer Sciences, or FCS, in an effort to dispel the impression that home ec was about teaching girls how to be housewives.