Admiralty Island, off Alaska, is a big island teeming not, as the name might suggest, with admirals; but with bears. Sixteen hundred of the furry monsters* wander around being ursine, befouling the woods, and outnumbering the human population by a ratio of three to one. Admiralty Island was originally named Fortress of the Bears, or in the native Tlingit language: Xoots-noowu, anglicised to Hoochinoo.
Anyway, in the eighteenth century a few europeans arrived there to trade furs (it was a bear market), and then in the late nineteenth century a lot of Europeans rushed over to search for gold. When they found that there wasn't any gold they cleverly decided to get drunk. This is where they hit upon the central problem of the whole island: a lamentable lack of liquor stores.
So the natives hit upon the bright idea of brewing their own booze and selling it to the despondent gold-diggers. The health-giving properties of this moonshone homebrew can be deduced from this 1915 citation in the OED:
They [the Chilcat tribe] were about to set out on an expedition to the Hootsenoos to collect blankets as indemnity or blood-money for the death of a Chilcat woman from drinking whiskey furnished by one of the Hootsenoo tribe.
Yeah. That kind of whisky. The good kind.
Anyhow, hoochinoo was a bit of a mouthful both literally and metaphorically, and had soon been shortened to hooch. And that, my child, is why we call cheap whisky hooch to this very day.
Our thanks to the wonderful people of Bear Fortress was to give them smallpox.
It should be noted that though a hoochie-mama may occasionally partake of hooch before engaging in hootchy-kootchy, the terms appear to be unrelated.
Incidentally, moonshine is so-called because it is brewed illicitly by the light of the moon. Moonshine can also mean nonsense or a month. As the younger and bastard brother Edmund says of his inheritance in King Lear:
Thou, Nature, art my goddess; to thy law
My services are bound. Wherefore should I
Stand in the plague of custom, and permit
The curiosity of nations to deprive me,
For that I am some twelve or fourteen moonshines
Lag of my brother?
Things the Inky Fool does when drunk
*It should be noted that I don't mind our plantigrade brethren except when they insist on nudity. I can't bear bare bears.