If the repairs are minor and the cost to repair them is less than your insurance deductible, you may choose to pay out of pocket to avoid any possible insurance premium increases that may stem from filing a claim.
Occassionaly, damages are not able to be seen until after repairs have begun. If you’ve already chosen to pay the cost of the repairs yourself, it will be too late to file an insurance claim. When accidents involve other parties and more extensive damage, you’ll want to file a claim with your insurance company and not the other party’s.