A definition we normally use is that a mod is an advanced e-cigarette that uses generic batteries replaceable by the user.
These devices can also be called 2nd-generation and 3rd-generation ecigs. They all have at least one feature that a mini (or 1st-generation ecig) doesn't have, even if that is just extended battery life or more available power due to the larger battery.
The Darwin is an exception to the replaceable battery qualification, as the battery pack is integral.
It is long past the time the term 'mod' was ditched, as these devices are no longer mods (of flashlights or copper tubing etc) in any way. It needs a suitable term that describes a short production run, full-featured, advanced, frequently expensive, 2nd or 3rd generation model that can cost between $60 and $250 or so.
Many suggestions have been made but nothing has stuck, as it didn't feel right. What it needs is for a manufacturer to hit on a snappy term like AVI or Advanced Vapor Inhaler or similar and stick with it, causing others to follow suit. Anything good gets copied pretty fast...