The difference is that, for most firearms, they don't keep some centralized database of ownership. Currently, if a firearm is traced, it has to go through its entire route of existence, from manufacturer to retailer to original owner to subsequent owners. If the trace leads to you, then you simply have to tell the ATF where and when you relinquished ownership of the firearm. It's not like, once you buy a firearm, you're responsible for every single event that happens with it forever. Think of the serial number like a postal tracking number and it might be more accurate.
That being said, some firearms are registered to a specific person, based on local law.