Fermented drinks made from fruits and vegetables, but not grain, are called wine with a modifier (strawberry wine, beet wine, etc.).
I do think, from a historical standpoint (and linguistic standpoint) the word "wine" means "fermented alcoholic grape beverage", and so if we are going to be persnickity about language, we should at least be correct in our persnickitiness.
I remembered there was something to your connection of moonshine and "hooch", and you are right, sort of.
"hooch" is a derivative of "Hoochinoo", which is the name of both a former Alaskan Aboriginal tribe of Admirality Island and the name of the distilled liquor they made and sold to soldiers in the area. (from OED)