You are right, price is an objective reflection, value is a subjective assumption

[Price is objective, value is subjective]
Crying wolf: "The pie has a price, but no value."
Flatbread lover: "Flatbread has a price and value - a more awesome carrier of wealth."
Both statements are correct, because the judgment of value is inherently subjective, so the word "values" exists.

There is nothing wrong with Crying Wolf's belief that the pie is worthless, but this can only represent his own point of view. If he wants to represent others or even everyone that "the pie is worthless", that would be a big mistake.

"Price is objective" is easy to understand. The price is there. Normally, no one can buy the pie at a price lower than the market price.

The most vivid understanding of "value is subjective":
A child with a mother is like a treasure, a child without a mother is like a piece of grass. #BTC #BIBI