Question about change of address

I went into the store and purchased my first firearm and am waiting for the NICS to be completed. My FID and my DL have the same address. For example purposes, my address is 123 Main Avenue. However my mom’s license has (example purposes) 123 Minor Avenue (I live with her currently) Both addresses are the exact same. If u look up either address, you get the same house. If you order something online with either address, it gets delivered to the same house. Main avenue is the mailing address and Minor avenue is the residential address. I am going to change my license to 123 Minor. Once I do, will I have to update my FID card? Even if both addresses are the same place?