Here's a potential difference - did you cause or contribute to the accident because of poor planning, flying, or negligence?
Or was the accident something that was unavoidable, like an engine failure in a SEL with no suitable place to dead stick into?
Two different scenarios. You said your accident did not result in a violation. It seems like you scenario is more likely the 'no fault' type. You still have to report it. Lying, and getting caught, is a ticket to being fired or never hired.