Schoolwork is the work you do for school: reading, writing, exercises, projects. It covers both the work you do in the classroom and the work the teacher sends home. Homework is only the part you do at home; schoolwork is the bigger pile. Parents and teachers use it when they talk about a child’s load — “She has a lot of schoolwork this week.” It is not the name of a subject. It is the tasks that come from school. People also stretch it a little: any heavy study can be called schoolwork, even exam revision at the kitchen table.