They aren't.
Typesetting machines, such as the Linotype, Monotype, Typograph,… are completely different devices than printing presses.
Typesetting machines rely on molten type metal (see here) to cast type. With a typesetting machine, the operator sets the text. A keyboard is used to set the letters in the right order, one by one. The machine than produces a certain output. In the case of a Linotype, the output is a 'slug', a line of text (see here), cast in type metal. In case of a Monotype, the output are individual letters cast in type metal.
Typesetting machines have nothing to do with ink or paper! The casted slugs or letters are taken out of the typesetting machine. Often, they are first put on a table, where a person composes the further layout of the page.
The composed page layout is then taken to a printing press. For very small printing presses, the printer will first put ink on the type before putting it into the printing press. For larger printing presses, the machines often put ink on the type. It's the printing press that puts the ink on a surface. The surface can be a paper, but also cardboard or anything else.
On a side note, take care with the term 'printer'. According to the Cambridge Dictionary, a printer is 'a machine connected to a computer that prints onto paper using ink', or it also is 'a person whose job is to print material.' Using the term 'printer' to refer to a printing press is incorrect.
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