I was wondering what are the differences between plastic surgery and cosmetic surgery?

Very similar: Cosmetic surgery is typically performed for the specific purpose of improved appearance (elective), and is performed by plastic surgeons and other board qualified surgeons. Plastic surgery is typically thought of as reconstructive, i.e. Surgery aimed at improvement of function or damage repair. Plastic surgeons also often do cosmetic surgery and often advertise as such.

Very similar: Cosmetic surgery describes surgery performed to improve the appearance. Plastic surgery is any surgery done to shape or mold the body, and this includes cosmetic procedures.