They are all pretty much independent, the overall storyline is pretty basic (you are a bounty hunter, the Metroids are dangerous space creatures that you go after, but space pirates want them as weapons) and all the games have a slight twist on that premise.
And yes, it's the same genre as HK (you find upgrades that allow you to backtrack and find new parts of levels) though this is more like an FPS version. But as per usual Nintendo, they do 3D versions of classic games/genres better than most, and this is no exception.
I kind of want to tell people to play with classic controls, as it was never supposed to be a full on FPS...but I think that would put people off trying to get used to the old style. I just wish with Dual Stick they toned down the health/ammo pick ups and boosted the bosses a tad.