Like the typewriter these machines were children of the second phase of the industrial revolution which started near the end of the 19th century. The second phase of the industrial revolution is also called the Second Industrial Revolution. This second phase brought to mass markets things like the small electric motors and the products of industrial chemistry without which the duplicating machines would not have been economical. By bringing greatly increased quantities of paperwork to life the duplicating machine and the typewriter gradually changed the forms of the office desk and transformed the nature of office work.
Self-publishers used these machines to produce fanzines, and they were also much used in schools, where cheap copying was in demand for the production of newsletters and worksheets.
Mimeo machine (mimeograph) used (heavy) waxed-paper "stencils" that the typewriter cut through. The stencil was wrapped around the drum of the (manual or electrical) machine, which forced ink out through the cut marks on the stencil. The paper had a surface texture (like bond paper), and the ink was black. It did not smell. You could use special knives to cut stencils by hand, but you couldn't really hand-write on them, because any loop would cut a hole, so you'd have a black blob. If you put the stencil on the drum wrong-side-out, your copies came out mirror-images.
Ditto machine (spirit-duplicator) used "ditto masters" that were two sheets together that you could type or hand-write on. The second sheet was like carbon paper (with the inked side up instead of down) that inked the markings on the back of the front sheet. The front sheet was then torn off and wrapped around the drum of the (manual or electrical) machine, with the back (inked, reverse) side out. That was the one with the solvent that could knock you out. The usual color was purple, but there were also a few other colors -- "red" was really pink, "green" was mint, "blue" was aqua. The paper was slightly slick or shiny, like cheap copier paper now. You could make multi-colored designs by doing different parts of it with different colored carbon/inking sheets, because the duplicating fluid was not ink but a clear solvent that dissolved just enough ink to print each sheet as it went through. Ditto masters couldn't make as many copies as a mimeo stencil could.
The same "ditto masters" worked on the spirit gum machines used before the rotary ones came along. Instead of a drum and a fluid, those were a metal frame (just larger than a piece of paper) with a roll of orangey-yellow gummed material stretched across it. You pressed the inked side of the ditto master against the gum for some number of seconds, peeled it off, and then pressed, by hand, each piece of paper onto the bed of gum, and it transferred the design. When you finished that one, you cranked the roll of gum material to the next position, like film in a camera.
The duplicating process involved the use of special pre-prepared waxed sheets, and a solvent with a distinctive odour. It was a messy, tedious and inaccurate process, which required a high level of skill from the operator to produce legible results.
The copying process involved: