Belief. Belief (on a collective, mass scale) is what separates one thing of value from another similar thing that has less or none of that same value.
What separates Gold's value from that of "fools gold"? Belief, further reinforced by it's attributes. That eventually becomes a self-reinforcing feedback loop that grows to a mass scale. That's it.
How did Gold get it's value as money and store of value in the first place? The first 100 people that started using Gold as a barter/money first believed in it, when no one else around them did. And then the discovery of Gold's attributes further validated that belief. And then the belief spread to 1000, then 10,000, then 100,000 people. Then around the world.
Belief is not what gives value to gold or anything else. Gold has value because of its intrinsic properties and rarity. It is useful for making jewelry, among other purposes in different industries. Fool’s gold does not have this value and it is far more common.
This feedback loop that you described is 100% real in many assets, including bitcoin. You are spot on in your description of how it works, but you failed to mention that if price is driven up simply by demand (or “belief”) and not by intrinsic value, then that is how bubbles form (and eventually, inevitably pop).