Basically the Welsh were the descendants of the old British inhabitants of the island who had been driven into the Western mountainous areas by the Saxon invasions. They maintained their independence from the Saxon English, but then along came the Normans and their successor dynasties who extended control over much of Wales. Edward I (of Braveheart fame) cemented this process by establishing great castles such as those at Caernarfon Harlech and Conwy. Edward started the practice of naming the first born son of the monarch as the Prince of Wales.
Given that the tax and spend policies of the Kings of the time made Margaret Thatcher look like Mary Poppins there were a number of revolts by the Welsh against their English overlords. The last and greatest of these was led by Owain Glyndwr in 1405. After initial success he, or at least his head, wound up as a permanent resident of a spike in London.
Within 10 years Welsh bowmen were fighting for Henry V at Agincourt.
The Welsh list on the book is a very limited time scale. The English lists in the PC game are from peak periods from the printed lists. Basically when there is the widest range of troop types. So we could have an English list for 1405 but it would just be a sub-set of another English list with fewer choices available and would be unlikely to be selected. Keith