Originally type faces were cast in metal from matrices by hand in a two piece mould (Gutenberg’s contribution) and then later by machine. For excellent images see this Website.
Above: A punch, matrix, one mat after the strike, and one finished and ready to go in the mould, and type— the way it comes out of the hand mould before finishing. The process is difficult to describe in words; the mould held in one hand while the molten metal is poured into the mould; at that moment there must be a motion made upward with the hand to force the metal down into the matrix. I am searching (looking through boxes) for a book which has some good images to post for this.
Here are images of Ludlow mats; two showing the font casting side, in stick; one showing the top side in a box. I’ll make some more pics of the mats in there cases as they are in the banks. The Ludlow is unique in that mats are set by hand in the stick and then cast in the machine which pumps the metal into the mats.