You are right in what you say, it is for this reason that when some markets are compared with Bitcoin they do not have much relationship, that is, when an analysis of the BTC market is made with respect to gold, they do not have any correlation, when it is done a correlation of BTC with the stock market there is also no correlation that can be extracted.
The precious metals sector has seen some correlation with BTC in the past. Although we cannot be 100% sure that the movements were correctly interpreted, but usually when the crypto market dips to a smaller extent than a huge crash, there is an uptick in gold prices and when there is a massive (>15%) selloff in crypto, gold and stocks both drop.
But when a correlation is made with both markets, gold and the stock market, if there is a correlation, they are similar markets to each other but with many differences in terms of concept, but there is also another peculiarity, when a correlation of btc with gold is made and the stock market there is a correlation but in the very short term, this is something that shows that the btc represents money but its deflationary nature and that it obeys other economic principles makes it move away from these.
The demographic difference is there. Gold traders are usually veterans in commodities trading. They usually did not try their hands in cryptocurrencies yet. Also the gold trading is not based on holding but on regular buying selling. So on the asset front, both might seem like high value assets, but their market psychology is different.
For the time being, since there is bitcoin minting still happening, we can keep aside the deflationary statement. With that, the average daily movements on bitcoin is higher than stocks.