Lots of models use various cartomizers of different threadings and ohms.
KR808D-1 can only use KR808D-1 cartomizers without an adapter
Fat battery ecigs and mods 450mah+ can use LR (low resistance, low ohms) cartos below 2.5ohms
KR808D-1 is the model you have (not 510, not 801, not RN4081)
Halocigs G6, SmokelessImage Volt, Bloogplanet Maxxfusion should all the the same style of KR808D-1
Vapor4life.com has been around a LOT longer and sells nice colors of a model more like the original manufacturer KR808D-1
Some minor other rebranders V2, Cig2O, Cig2Go - I think those are KR808D-1 threaded
And then there is the plain original manufacturer KR808D-1
And you should be able to use cartos from the above
The Provape may be KR808D-1
The Cigeasy Easy says it is compatible with KR808D-1
For adapters, the abbreviation for KR808D-1 is 808
901 atomizers will fit without an adapter and like any slim ecig, you would use standard resistance, not LR.
If you have manual batteries you can pretty safely use a drip tip on the 901 atty to test juices. Else use carts.
And you can use any KR808D-1 cartos 2.5ohm or higher.
There is also an INCOMPATIBLE KR808D-2 aka E9 sold by some rebranders - not compatible with KR808D-1 (so any model that LOOKS LIKE KR808D-1 is not necessarily KR808D-1)
Mini is just the length and being slim. 100mm or longer and slim is mini but not all minis are good real minis. There is at least one super-mini that has one longer battery size that makes it over 100mm. But it is still skinny with crappy annoying tiny cartridges like a super-mini.
The main minis are around 9.2mm thick. 901 (which is a 3-piece) is the only one with threading the same as KR808D-1 but it expects its airflow to come in through a hole in the side of the atomizer and has few cartomizers made specifically for it to the point where cartos are hard to find. 801 is a pen style 3-piece with another threading. 510 is a 3-piece with yet another threading (and the most things are made for 510 threading if you include all of the LR stuff, KR808D-1 having second most). RN4081 is the only other semi-popular 2-piece but is has very weak market support compared to KR808D-1. KR808D-1 is the most popular 2-piece mini.
Above minis are fat battery models and mods.