"hedged fund" implies that the fund itself is hedged. It is the original and correct term (hence the link).

"hedge fund" implies that the fund IS a hedge (presumably against other assets one might own). Except that in and of itself the fund cannot hedge you without knowing what you own.

Nowadays, everything is called a "hedge fund" incorrectly - they should be called "hedged fund" as per the original term. They provide diversification and hopefully some return above CPI, or some well-defined risk-adjusted return.

By the way, "hedging against volatility" doesn't mean much. Most of those funds are short volatility.