Their economical definitions: Benefit is a payment made or an entitlement available in accordance with a wage agreement, an insurance policy, or a public assistance program. Profit refers to the return received on a business undertaking after all operating expenses have been met.It is in other words the excess of revenues over outlays and expenses in a business enterprise over a given period of time, usually a year. Otherwise both 'benefit' and 'profit' could also mean the same,referring in general to any advantageous gain or return.

Cheery's reply is great, though I personally think, we are more likely to use benefit unless money is involved.

benefit = any good outcome profit = a good outcome regarding money