Option 1 (recommended):
Choosing "I would like to list my products under my own brand , GTIN exemption" :
Suitable for seller who:
selling items without identity like UPC\EAN\ISBN
would like to use his own brand name while listing the items on Amazon
sells items which are not already exist on Amazon.
sellers which would like to list items under their own brand name on Amazon without using bar-codes.
If you are the brand\manufacture owner of your items you can register as a brand on Amazon, which allows you to use an alternative product identifier such as Part number (if you don't have part number our service will generate it for you )
It let you list your items without their formal bar-codes and under your own brand name (that you choose) .
No one can use your own brand after register as a brand on Amazon except you.
Please read this Amazon article about GTIN exemption.
You can enroll your brand in the Amazon Brand Registry later Here.
Example for choosing the option 1 above (very common):
I own an eBay store called "Old but Gold parts" and I'm selling car parts ( Ford , Audi , Subaru and more..).
I should choose option 1 exporting my items using GTIN exemption with the brand name "Old but Gold parts" (for example , my own eBay / Amazon 's store name recommended as brand name).
* This example is correct for all categories and similar situations
Option 2:
Choosing "I would like to use one or more brands which are not belong to me, I have bar-codes for those items":
Suitable for seller who:
selling items that exist on Amazon and would like to match his items to the same ASINs.
Have bar-codes (UPC\EAN\ISBN) for all his items.
Would like to match the items to existing ASINs (items) on Amazon and have their official bar-codes and SKUs.
Example for choosing the option 2:
I own eBay store and selling my own official products with their official bar-codes and would like to list them on Amazon using the same as on eBay (also with the same brand name as on eBay)
Or
I have official products that already listed on Amazon and I would like to match them to the same ASIN on Amazon, also I have the same SKU, official bar-code, brand name and title as on Amazon.