The most common one is packaged and sold by Joshua Roth Limited and as you indicated, is only listed as Kyoto Moss.
If they know the species of moss they are selling, It is a closely guarded secret.
Could be anyone of about 2 dozen (or many more) species. that is commonly found around the Gardens & Temples in Kyoto and is known as Kyoto Moss.
Here's a link to a vendor of Bonsai supplies that offers the spores.
Rb

Here is a link that might be useful: Kyoto Moss

The species Leptobryum pyriforme may be what is being sold as Kyoto Moss. This from a statement in Janice Glime's text linked below. Reference is on page 12

Here is a link that might be useful: Janice Glime : Ecnomic and Ethnic Uses of Mosses