It's a charm. It's under the charm listing of things, just like Stupefy is.
Different spells allow for different tactical considerations?If there is no difference in DC for the two spells why bother making two options? Harry should know how the spell works, which is why I asked for confirmation.
Expect when it doesn't. In the book canon, most spells (I think) are never explicitly described as a beam or anything. I'm pretty sure the levitation charm didn't ever mention anything of the sort.
Spells go where you point your wand. AK shoots out of a wand. Stupefy (a charm, like the Homorphus Charm) shoots out of a wand. Cruciatus shoots out of a wand. Cutting charm? Wand. Legilimens? Unless you're really fucking good at it, Wand. Even the levitation charm, which doesn't show a beam has a direct correlation between wand and target. You move your wand, the targeted item floats according to the location of the wand.
The wand, and wand movements are critical parts of spell casting. If they weren't important, everyone would be casting wandless magic from anywhere at all. Why bother aiming when you can just make your spell appear in someone's head.