Gorilla Glass is harder than the metals used for keys and coins, or even most knives. This means it's easy to produce marketing videos showing how "tough" it is, and to be fair you don't have to worry about keys or coins scratching your phone screen. But ordinary household grit contains mineral particles that are much harder than those metals, so it's perfectly possible to scratch Gorilla Glass just by putting it down on a table if there is a bit of grit under it. I have done this myself with a new phone screen: put it face down during a meeting, shifted it slightly, found it was scratched.
Sapphire is much more scratch resistant, which is why it's used in many watches - but it's also more expensive (which is why it isn't used in cheap watches).
Polishing out scratches requires using an abrasive to wear the surface down a bit and make the scratch less visible. If you think about it that means that the abrasive (e.g. crystals in the toothpaste) is harder than the surface you are polishing, which also means that a larger piece of the same material could scratch the glass.
On the subject of toothpaste, they vary a lot in how abrasive they are, so daft as this sounds it might be that you'd have more luck with a different brand. However polishing only works for shallow scratches, you won't be able to polish out a deep one.
