Difference between homework and study in Korean
숙제·공부

숙제homework
Homework (숙제) is school work that students do after class, often at home. It can be math, reading, writing, or other practice from the teacher. People often say they have homework, do homework, or finish homework.

공부study
Study means learning something by reading, listening, practicing, or doing homework. In Korean, 공부 is used when you study a school subject, a language, or prepare for a test. You will often see it with the verb 'do' to mean 'to study.'
The difference
공부 means studying in general. 숙제 is a specific task your teacher gives you to do after class.