고장나다(go-jang-na-da, gojangnada)
When a machine or device breaks down and becomes unusable.
When to use
machine breakdown, electronic malfunction, unusable state for devices, not for people
The nuance
Use 고장나다 when a physical machine or electronic device loses function due to internal problems. It is not used for people or abstract situations.
멈추다(meom-chu-da, meomchuda)
When a machine or person stops movement or operation, temporarily or permanently.
When to use
machine operation stop, temporary halt, person stops moving
The nuance
멈추다 is used when machines, people, or situations stop moving or operating, either temporarily or permanently. Unlike 고장나다, it does not necessarily imply malfunction.