Yes , that is it in a nut shell... it is mostly agreed that tamahagane refers specifically to steel smelted in Japan of Japanese iron bearing sand, and smelted in a tatara oven.
The vast majority of nihonto (true Japanese swords) are(were) forged from tamahagane, which is folded repeatly to make a homogenized billet , then the billet is drawn into a sword, ande laminated with different carbon content steels in one of various lamination techniques, including hon san mai , and others...
The exception to Japanese swords being made of tamahagane include shingunto and showato (WWII era swords) and a few antiques containing a percentage of nanbantetsu (barbarian steel) .
Further it is usually agreed that steel smelted in the fashion of tamahagne , but off of Japanese soil is to be called Oroshigane, but the lines are becoming blurred by western masters that are smelting and working in tamahgane type steel , including Jesus Hernandez, Anthony Di Cristifano, Walter Sorrells and the late Paul Champagne.
There is a trens noe for various production companies to offer tamahagane swords, including Hanwei, and Dynnasty Forge, but IMHO it is not worthwhile to buy these. Yes the tamahagane is what makes the beautiful pattens called ji-hada in nihonto... butg it is brought out by a master polisher, that has apprenticed 15 years to learn his craft...
IMHO without a art level polish to show it off, tamahagane is not as desirable as modern steels....
