Both refer to the fact that the individual has stopped living. It’s the manner in which this event happened that differentiates the meaning of the two words.
`Killed’ suggests that the death was not due to natural causes. For example, when you say, `The minister was killed in her sleep’, it suggests the person was murdered while she was asleep. Someone did something that resulted in the minister’s death – maybe the person stabbed/shot/smothered the minister while she was sleeping. `Kill’ suggests that the death was caused by some external agency — it was not natural.
When you say that someone `died’, what you are implying is that the individual’s death was due to natural causes – there was no hanky-panky involved. No one was the cause of his/her death. `Died’ is not as strong as `killed’.