Based on what I know, asahi glass, Japanese grade 1 glass, float glass all refer to the normal glass we see, slight greenish cast. Maybe different brands from different manufacturers so all have different names. To me, they are all the same.
Crystal glass, starphire glass, low iron glass refers to optically superior glass. Again may have slight differences between them, but to me they are pretty similar.
I may be wrong, so if there are glass experts out there, can point out the finer differences to what I have broadly classified as 2 categories.