A stablecoin is a form of cryptocurrency thats value is fixed by pegging it to the price of another asset.
This is how exactly stable coins are but not correct if you see it another way arround. With this definition, wbtc, rbtc and many pegged tokens like that are begged with bitcoin, they are mimicking the price of bitcoin, but are they stablecoin while their prices are stable with bitcoin price but they are not stable coins. I believe the real name people should call this stable coins are
fiat-pegged coins. They are called stable coins, but practically they are not stable, they follow the value of fiats. If fiat devalue they will also devalue.
The real purpose of stablecoins is to make your coins fixed at a point that you convert.
Stable coins are not having fixed price, they are only pegged with fiats like you quoted above.
During the current bull, many hodl their portfolio in stablecoin and I believe this is a very wise think to do and stable coin is the reason that people are seeing cryptocurrency as having fiat relation and impart in terms of value and stability.
Yes, that is how it works with cryptocurrencies, fiat pegged coins are safe haven when unstable coins are falling in price, while unstable coins are converted back to if bull run has started.