Presses that operate plane to plane are called platen presses. A vertical clamping contrivance clamps the bed, which carries the form into which the composed type is locked, and the platen, which carries the sheet of paper while it is being printed.
https://en.wikipedia.org/wiki/Letterpress_printing
* https://handsetpress.org/equipment.html
* https://handsetpress.org/liberty/
https://letterpresscommons.com/platen-press-history/