I understand during the recordings that they usually used either a wax recording disc that would adjust to the pitch of the music being played, but how did this happen for mass production? Some sort of machine that read the master and used the crescents and dips of the grooves to grind the same pattern into the new LPs?
Disc records are made in a process called press molding. Think of it like a giant waffle iron. Each side of the record has a metal mold, which is called a stamper. A puck of vinyl plastic is put between the halves of the mold, and as it presses together the plastic is heated and flows into the grooves.
The creation of a master disc and stampers is a complicated process. I hope it doesn't violate the rules of this forum by posting the links, but it really can be best explained by watching these videos: https://www.youtube.com/watch?v=xUGRRUecBik&t=33s https://www.youtube.com/watch?v=IReDh9ec_rk&t=216s
The major difference historically is that record companies wouldn't discard the lacquer masters, as they say in the video, because they could reuse them. Also, they wouldn't make stampers directly from the lacquer master. They used the first metal disc to make sub-masters, called mothers, which in turn were used to make the stampers. In records heyday, they needed multiple lines of multiple stampers for the same record as popular ones would sell millions of copies.