The Bronze Age Huntress was Bruce and Selina's daughter from Earth Two, the same universe as Power Girl (who's normally an older alt universe Super Girl, not a Super Girl clone like in the Justice League show and Something Unlimited).
After Crisis on Infinite Earths, Helena Wayne was removed from continuity and there was a new Huntress, Helena Bertinelli. The new Huntress has the same costume, but a different personality and backstory, being the daughter of a mob boss who's entire family was taken out by other members of the mob and she swore revenge against the mafia in general.
Helena Wayne was brought back in the New 52, though with a somewhat revised history, such as being the only Robin under her father and being a bit more ruthless.
Fun fact, Artemis's mother Paula was originally a Golden Age super villain named Huntress, Tigress being a retroactive name given to her when she was brought back in the 80's in a series about her as a hero before later becoming the villain Huntress. The original version of Paula was Caucasian and not Vietnamese (being Paula Brooks rather than Paula Nguyen), as Cheshire being her daughter was a change made for Young Justice. Sportsmaster being her husband and Artemis's father is from the comics, though.
Got a little off track there