Most car repair parts are invisible once they're installed. More to the point, most people couldn't tell the difference between an OEM (original equipment manufacturer) part and a substandard, under-the-radar generic part made by a metal-stamping plant that has seen better days.
Your insurance company, however, knows the difference. Generic parts are cheaper, often much cheaper, than OEM parts. That's not to say generics are necessarily inferior (think generic drugs), but they can be.
It's really important that you get your car fixed at a repair shop you trust. You need to have confidence that whatever parts are used, your car functions the way it did before it was damaged. That's your right.
Check your car insurance policy to see if it specifies the type of repair parts that the insurer approves for work performed to settle an insurance claim. If it doesn't, or if you have any questions, call the company or your insurance agent for a clear explanation. Sometimes, you can add a rider to a policy that specifies repairs must be done using OEM parts. You might pay a bit more for the policy but that may be worth it to you.
Minimum standards for repair parts are spelled out by some, but not all, states. If this becomes an issue, check out your state insurance department and find out the standards that affect you.
Regardless of what a policy says, there is no way you should ever be forced to accept substandard repairs or parts. You might get into a spat with your insurer here, but you can push to make sure repairs are done to your satisfaction, including using OEM parts if the generics do not fit or function properly. This is yet another reason why you need a mechanic and body shop that will provide you accurate and honest feedback on the quality of the repair parts used to fix your vehicle.