'work at' vs 'work for'

[Daemon99]

1) I work at IBM
2) I work for IBM

Is there a difference between these two sentences? Are they both correct?
Please help.
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Non-native speaker of English
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I intend to live forever - so far, so good.

[Torsten]

Both sentences are correct and they can mean the same thing: You are an IBM employee. Then again, there can be difference: If you work at IBM, your workplace is at the IBM premises. If you work for IBM, you can be a self-employed free lancer who has a project based contract and is working at home.

TOEIC short conversations: Catering employee calls customer to inform her about a delivery problem.