It means that the component underwent testing under specific Automotive standards and passed.
It doesn't mean that the non-Automotive component would not pass as well, it just wasn't tested.
If it is exactly the same component, you pay a bit extra for the automotive qualified component to compensate the manufacturer for paying for the testing, and you get a certificate that you can show to your customer. If your customer doesn't require the certificate, then buy the exact same component, not certified, and save a bit of money.
If it is not exactly the same component, then the automotive certified one is more reliable when used under the challenging automotive environment. But, if your product does not experience that same environment as the automotive one, then that certification doesn't necessarily tell you whether that component will survive longer in your product's environment or not.
EDIT:
are there any negatives, other than money?"
Possibly: an Automotive Qualified component that does not address issues that are not an issue in the automotive environment, such as low atmospheric pressure, deep sea pressure, ionizing radiation, or strong EMI, may actually be less reliable than a non Automotive Qualified component when used in environments other than automotive. For example, a wire-wound resistor (not Automotive Qualified ) may perform better in a nuclear application than a metal film resistor that is Automotive Qualified.
(Unlikely, but possible.)