Thompson’s seedless was indeed the first commonly grown in the US. Other seedless grapes commonly grown in this country were created from crosses with Thompson Seedless, Russian Seedless, and Black Monukka in the 20th century.
The original push behind the need for seedless grapes was for the raisin industry, because people hated to have to seed raisins before using them. In fact, I distantly remember from when I was a child in the 1950’s that we could buy some unusually large raisins out in California, but they had seeds in them.
A breeding program to produce seedless grapes was begun by the New York State Agricultural Experiment Station in 1919 but was most successful in the 1950’s with Glenora (1952) and Canadice (1954).
Dr. H.P. Olmo, a professor from UC Davis came up with a lot of them. He was a sort of horticultural Indiana Jones. He came up with the Perlette grape (a seedless grape similar to Thompson’s but with a wider climate range) and it was released to growers in 1946, then in 1959 he developed a black seedless grape, followed by Ruby Seedless and Beauty Seedless, but they weren’t released to growers. He developed Red Globe seedless grapes (one of my favorites) somewhat later from grapes he discovered in Afghanistan, and they were released to growers in 1981.
In fact, as recently as 1990 the Russians came out with yet another type of seedless grape, the Rusbol.