Native iso is "the sensitivity you get without amplifying the analogue signal you get from the sensor". Unity gain ISO is "the ISO of the camera where the A/D converter digitizes 1 electron to 1 data number (DN) in the digital image." They both seem to be the same but the unity gain ISO is unique for each camera whereas the native iso is a range of ISOs. If no amplification means assigning 1 digital unit to 1 photoelectron, aren't both native ISO and unity gain ISO the same?
Whether this is where you found it or not, the definition you give for "Unity Gain ISO" comes from the Clarkvision web site's section on digital sensor performance. As an updated version of that page explains, it's a silly concept. To quote:
The fundamental reason Unity Gain is not relevant is because the sensor in a digital camera is an analog system, not digital. The signals from the sensor are analog and only after amplification is the signal digitized.
By definition, the analog signal does not correspond directly to a "count". It's simply a level. My basic advice is to not worry about at all.
My slightly more opinionated advice is: if you are hanging out on forums where terms like this are bandied about and debated, get up, walk away, pick up your camera, and go out and shoot. If your images seem noisier than you'd like, get more light. If that's not possible, photograph something else.
Unity gain is such ISO number at which camera outputs pixel values roughly equal to numbers of electrons in cells.
Native ISO is such ISO value at which the maximum number of electrons in cell is matched to saturation point. It is almost always division instead of multiplication for sensors with big enough electron capacity per cell. Native ISO is as unique for each camera as well as unity gain ISO is.
Modern APS-C sensor cell capacity measures 60000+ electrons and this potential cannot be used with ADC outputing only 16384 levels. So, division is used (however it would be incorrect to say "division" about CMOS image sensor because CMOS sensors always amplify the signal for it to be measured, i.e. the number of electrons passing through the ADC for a pixel is many times higher than number of electrons the pxiel's capacitor holds).
14 bit ADC will probably never be used in division mode for 1" or so sized sensor.