There is no literal term for the word Ţuică , its use depends on region. But technically this is a simple classification:
Ţuică = generic term for distilled alcoholic beverage
Palincă = thrice-distilled plum brandy
***Horincă = twice-distilled plum brandy***
Jinars = twice-distilled plum brandy (Transylvania - Cluj)
Făţată = the strongest brand, twice-distilled

http://en.wikipedia.org/wiki/Ţuică

Sau double-distilled plum brandy:

In Maramures, a forested northwestern corner of Romania surrounded by the Carpathian mountains, the drink of choice is ***horinca—a double-distilled plum brandy*** prized for its clarity and its 80-proof wallop.

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