My view on this is that wealth is something real that actually impacts people's lives. At the same time money is not, it's the story told around wealth so that we can all agree on how one "wealth" compares to another. The goal is to not let this story go wild (e.g. into super-inflation) so that people don't lose trust in money.

Keeping those two in check is the main goal of any central bank, ever since the gold standard was generally abandoned and money became entirely abstract. In my opinion no one really knows how to do it (although it's been okay-ish so far), the FED for example often uses national unemployment rate to decide how much dollars should be thrown at the system.