노동자 is the traditional term for "laborer". It can mean manual laborer in a narrow context but it can also refer to any worker who does work by exerting themselves.
근로자 is a less frequently used term that just means "worker". Since 노동자 has acquired the connotation of laborer as someone who fights the management (as in 노동 운동 = labor movement), governments and other organizations often want to avoid those political overtones and 근로자 fills this need nicely. For instance, 근로자의 날 is Worker's Day. It is a textbook-like term mostly used in very formal contexts.
There are numerous words describing work and job. I'll list some common ones.
Common verbs.
- 일하다 = to work (most general and widely used term).
- 노동하다 = to labor. 육체노동자 = blue color worker. 정신노동자 = white color worker.
- 근무하다 = to be on duty at work. 근무지 = workplace. 근무시간 = work hours.
- 작업하다 = to work on a task. 현장 작업자 = workers on scene.
General terms for "employed worker".
- 종업원 = worker/employee (sometimes implies employment status)
- 직원 = same, but more vague, a little like "clerk" or "person on hand".
- 사원 = an employee of a private workplace. More formal than 종업원 or 직원.
(All three are common terms describing employees of a workplace)
Terms for "worker" in general (and typically more formal).
- 노동자 = worker or laborer. Makes compound words like 부두 노동자 (dock laborer).
- 근무자 = person on duty.
- 작업자 = person working on a (well defined) task.
- 인력 = workforce.
- 관리자 = manager or caretaker.
- 노무자 = workers doing physical work.
- 일꾼 = similar to 노무자 but more informal (and somewhat disparaging).