【Accident】 , 【casualty】 and 【mishap】 are synonyms when they designate chance or a chance event bringing injury or loss.

【Accident】 is broadest in its application, being used of events that involve persons or things, or injuries or losses, serious or slight.

• he was crippled by the 【accident】
• a railway 【accident】
• owing to an 【accident】 to the machines one department was closed down

【Casualty】 commonly implies destruction, especially of life, and is chiefly applied to an individual whose death, serious injury, or even desertion constitutes a loss to a military (or similar) force engaged in hazardous activities.

• the regiment suffered heavy casualties

As applied to insurance 【accident】 and 【casualty】 are usually distinguished: 【accident】 insurance is a provision against injury to oneself through 【accident】 ; 【casualty】 insurance is a provision for indemnification for loss from 【accident】 (as fire or burglary) and especially for damages incurred through one’s liability for injury or loss to others.

【Mishap】 as a rule is applied only to slight accidents, especially those involving disappointment or frustration.

• a day seldom passes without one 【mishap】 or another

【Accident】 refers to an unforeseen event (good or bad).

• George’s call about the job opening was just a lucky 【accident】 .
• A flawed design contributed to the Chernobyl 【accident】 .

【Incident】 refers to a minor or simple occurrence (good or bad).

• The entire 【incident】 was recorded on video.

【Mishap】 refers to a minor unfortunate occurrence.

• Though no one was hurt, a 【mishap】 occurred during the parade.