How I see them is this:
"Unlicensed": An original game that did not get an official license or go-ahead from the console makers to be developed for the system. This term can be used in two ways:
A: A general term used for all unlicensed titles, bootleg or otherwise, as they are technically unlicensed. Harry Legend, Shi Kong Xing Shou, Menace Beach, Mario & Sonic 3, etc.
B: Unlicensed games that don't contain stolen material (or at least the stolen content is minimal, such as occasional overworld tiles from, say, Pokemon.)
For example, Color Dream's games don't steal anything, but they weren't authorized by Nintendo to develop for the NES system. Their Lynx game Crystal Mines 2, however, was officially licensed, so it technically doesn't count. However, since it's related to an unlicensed company, it will sometimes be brought up when discussion about the company rises (basically for the sake of info).
"Pirate Original"/"Bootleg Original"/"Pirate"(etc.): Similar to the previous, but it contains copyrighted material that was used without permission by the right holders. Games such as Somari and Digital Monster 3 are examples, as they contain copyrighted material owned by someone else, but are original productions.
"Hacks": Games that were originally developed by a different company, but then rereleased with minor enough changes made to the game to where they aren't considered their own title. Hacks can be either official (which I'm assuming many Hacker International titles were) or unofficial (such as Pocket Monsters Go Go).
