Where I live (PNW), we have “local grass hay” that can be anything at all, of any quality, grown in the coastal rain belt by small farmers, which you can buy from the field or have delivered. Then we have timothy and alfalfa that are grown by commercial producers, in the dryer areas in the interior, and you buy from either a hay dealer or through a feed store. Timothy tends to be 3 string bales, and the hay that is transported down to the coast, at least, is much more standard in quality.
That said, timothy is not necessarily lower in NSC or finer or coarser than the other grass hays. It all depends on when it was cut in the growing cycle, and indeed even on the time of day, like all grasses. Mature timothy can be stalky, but younger timothy can be leafy and green, and not even have the characteristic inflorescence present yet.
IME, having looked at tests for various hays, palatability is related to the fineness of the hay, but the fineness of the hay is not related to the NSC content. So you can have very nice, fine, soft hay that your horses love, but it is not necessarily high sugar. And you can have coarse, stemmy, mature hay that is also high NSC. The “coarse pony hay” (local hay, a mix of random grass and some timothy) I had tested a few years ago had 24 % NSC, which is crazy high. I don’t know how much of that sugar was nutrtionally available, given that the ADC (undigestible fibre) was also high. However, I do think this hay was connected to a small pony (not under my care) eventually foundering. The very high NSC hay (both coarse first cut and finer second cut) from this same farm did also tend to give my mare diarrhea, which I think was related to the NSC levels. And I also find, now that I am not feeding it this year at all, that my mare is not tending towards obesity quite as quickly. Her weight is staying stable on more hay than when I was feeding the high NSC hay.
This year and last, I’ve ended up mixing nicer “local” grass hay with commercial 3 string timothy, and the timothy is very, very, nice. But I think this is as much to do with the fact it has been well made, in a better hay-growing region, as it has to do with the actual species of the grass.