Yes, those that occur in the wild in nature.
But, some sub-populations are isolated. The species on Yakushima island are apparently morphologically distinct from mainland species. And then there are purple flowered mutants, when most are actually red. On top of that, there are areas where R.indicum and R.eriocarpum/tamurae habitat overlap each other, and there natural hybrids can be found.
Yes, it is an umbrella term.
Not all satsuki are hybrids or forms with interesting horticulture properties. In a sense, there is 'the' R.indicum. I would say that 'Osakazuki' is a purple form of 'the' R.indicum. And reverted 'Kinsai' can also be called 'the' R.indicum.
Every cultivar has a name. If you want to see species, ie wild-type, you can go to a botanical garden.
As for what really is 'the' R.indicum, you can get the genome sequences for like 80 to 500 euro/dollar. If you do that, you will find there is no 'the' R.indicum.
I just decided to order the 2014 dictionary. I guess I am 3 years late, and in 1 to 2 years, the 2018 version will be on the market. My 2010 version is kind of worn out.
I don't remember ever seen a variety in my 2010 dictionary that is claimed to be of R.nakaharae descent. I myself have some 'Kozan' x 'Alexander' seedlings. And Dr. Tsuneshige Rokujo send seeds of those crosses to the US. So Japanese were experimenting with them.