"Double flarel" and "inverted flare" are not separate "qualities."
There are different ANGLES of flare. AN also similar to JIC fittings..........AN is originally "Army-Navy" (at the time there was no air farce) and typically aluminum, originated mostly on aircraft. The are 37 degree flare angle and can be either double or single flare
SAE flare is what you see common in "traditional" auto parts stores and hardware stores. These can be any material but commonly are brass. They are 45 degree flare angle and can be either double or single flare.
Inverted flare is I think a stupid name. SAE flare and inverted flare USE THE SAME FLARE on the tube. Only difference is fittings. SAE 45 flare is a female nut that fits a male flare adapter. INVERTED flare is like brake tubes.......an male thread nut into a female adapter.
Single / double flare..........Single flare is when you put a piece of tube in a flare tool and flare it in one simple operation. This leaves the cut end of the tube "at the end" and is thus liable for irregularities and more important, SPLITTING at the end
Double flare is like a hem on clothing. The special tool upsets the tube in sort of a barrel shape and then that adapter is removed and finishes the flare by mashing down the flare so that the raw edge is on the back
Google stuff like "using a double flare tool" and you'll see
Bubble flare is sort of like "the start of" a double flare but the thing is not completely mashed down. I don't personally like them and see no purpose for them. I think they originated in Europe, AKA Vee Dub and the sickness spread from there.
Google up a fittings catalog as I mentioned earlier and look through it
https://www.eaton.com/content/dam/e...ctors/Eaton_brass_products_master_catalog.pdf
