For practical purposes, these days, I believe a "hedge fund" is basically defined by its high fees (2&20), lack of regulation and disclosure compared to a mutual fund, and its restriction to "qualified investors" who are supposed to be wealthy enough to absorb losses. Certainly quite a few so-called hedge funds get a lot of publicity for the opposite of hedging - making wildly risky bets to try to beat benchmarks.
For anyone interested:
The term "hedge fund" originated from the paired long and short positions that the first of these funds used to hedge market risk.
https://en.wikipedia.org/wiki/Hedge_fund