This wasn't a remake right?

I wrote a post on this on my "Newcomer's Guide to Robert E. Howard" blog, hopefully this can answer your questions:

Right, so what’s this film then? Is it a sequel to Conan the Barbarian?

No. This film is entirely unconnected to the previous films, and is intended as a franchise reboot akin to Christopher Nolan’s Batman Begins, complete with a new origin story by Thomas Dean Donnelly and Joshua Oppenheimer, with tweaks by Sean Hood and Andrew Lobel.

Is it a remake of Conan the Barbarian?

No. A remake implies a film is based on an earlier film: this is intended to be a new adaptation of the Conan character, who first appeared in the pages of Weird Tales in1932. The story written by Oliver Stone and John Milius for the 1982 film is entirely original, and outside of a few scenes extracted from two or three Howard stories and adoption of some names and elements, it bears very little in common with Howard’s creation.

But if it isn’t a remake, why does the plot sound just like Conan the Barbarian?

It is true that the storyline bears a number of similarities to Conan the Barbarian: the young barbarian whose village is massacred, one of his parents murdered by an evil warlord with sorcerous power, and a quest for vengeance across the Hyborian lands all figure in what is known in the upcoming film:

Our protagonist is a young Cimmerian named Conan
His father is a blacksmith
His village is attacked by a band of raiders
His father is killed
The raider’s leader takes his father’s sword
Conan eventually resolves to avenge his father’s death and village’s slaughter
The rest of the film follows Conan as an adult

However, there are significant divergences too:

Conan is not enslaved and taken north; he goes south and joins up with a group of pirates
Conan is not chained to the Wheel of Pain for 20 years; he lives a life of piracy through to adulthood
Conan is not forced into pit fighting; he gains experience in real battles, not gladiatorial combat
Conan is not taken to the Far East to learn eastern martial arts; he learns how to fight naturally, not through schooling
Conan doesn’t discover an Atlantean Sword in a crypt; he uses whatever weapon suits his purposes
Conan is not crucified on a Tree of Woe
Conan does not travel to Zamora
There is no Black Sun Cult of Set
There are no Mounds of the Dead
There is no Battle at the Mounds
There is no Tower of the Serpent
There is no Mountain of Power
Conan is not resurrected by demonic forces and the sacrifice of a loved one
Thulsa Doom does not appear in the film
King Osric does not appear in the film
Valeria does not appear in the film: Katarzyna Wolejnio’s minor character is completely unrelated to Sandahl Bergman’s
Rexor does not appear in the film
The Witch does not appear in the film: Rose McGowan’s “half-human, half-witch” Marique is not the same as Cassandra Gova’s witch
Subotai does not appear in the film
The Wizard does not appear in the film
The Princess, King Osric’s Daughter, does not appear in the film
Red-Hair, the slaver who frees Conan, does not appear in the film
The “Mongol” General and Turanian Officer do not appear in the film
The Pederast Priest does not appear in the film
Thorgrim does not appear in the film
The Sword Master does not appear in the film
None of Milius’ or Stone’s famous dialogue is in the film
None of Basil Poledouris’ iconic themes and melodies is in the film
None of Ron Cobb’s production design is in the film
None of John Bloomfield’s costume design is in the film
None of Jody Sampson’s swords are in the film

.. in short, next to nothing from Conan the Barbarian, save the bare bones of a young Cimmerian’s quest for revenge for the murder of his tribe and parents, will be making an appearance.

As for why it's called Conan the Barbarian, well, the name predates the 1982 film in a number of ways: it was the name of one of the original Gnome Press collections and later Lancer collections; it was the name of the popular Marvel comic. Eventually the very name Conan the Barbarian became shorthand for the character.