+1 on this.
Unfortunately there is correlation between Bitcoin and US stock market, in terms of their price, even though the same doesn't seem to be true for gold.
You have a skewed view on this IMO. To begin with, the supposed correlation only exists in the short term, if you zoom out you will see that there is no such correlation. And if we go to the most recent the price of bitcoin has remained fairly stable when the stock markets have plummeted. If you think about it, as volatile as bitcoin is, it would have fallen much more if they had been correlated.
Bitcoin is priced as an asset and not as a currency, that's why it happens. I am not implying that gold is a currency nowadays, but it's obvious that the fact it used to be a currency, still has some importance in terms of their correlation with the rest of the US markets.
Both bitcoin and gold are financial assets and as is normal different financial assets behave differently even if at times the price behaves at par.