I don’t think there is a standard definition of a hedge fund.
I always thought the so-called hedge fund had a much wider latitude with their investors, such as the use of options, shorting stocks or indexes, venturing into forex or commodities when warranted, etc.
But I’ve been told I’m wrong (although no one seems to know what the right answer is).
https://en.wikipedia.org/wiki/Hedge_fund
I thought this was quite informative, although there are certainly other perspectives.