At first, unit-set type (q.v.) and point-set type seem nearly the same. One might think that point-set type is just unit-set type using points as the basic unit. But this is wrong, and misunderstands the theory of unit-set type.
In unit-set type, a basic unit is first selected. Typically this unit is related to the body size. This unit is then subdivided into some reasonable number of parts (e.g., 18) and all type is cast to integral unit or simple fractional unit set widths. These units need bear no direct relationship to any point system (indeed, the first unit-set types predated the American point system).
In point-set type, there is no basic unit at all. Point-set type, for all its apparent simplicity, is an ad hoc system where type is simply cast to set widths which are of integral or simple fractional point dimensions. These point-set dimensions have no direct relationship either to each other or to any controlling unit.
In his biographical sketch of Julius Herriet, Jr., Loy notes that Herriet cut (but did not design) "several sizes of Mural and Façade, some of them to the point set and uniform-lining system, which had been advocated in a series of articles written by N. J. Werner and published in Artistic Printer."
By at least 1897, the Inland Type Foundry was advertising "Unit Set Type" (with, additionally, their "Standard Line" of uniform vertical alignment). See The Inland Printer, Vol. 20, No. ? (1897): 358.
For more on this, see the The Inland Type Foundry section of the Unit-Set Type Notebook.
By 1899, they were advertising "Point-Set" type. See "Explanation of the Improved Point System" within a type showing in an advertisement for "Point-Set Old Style Series / Old Style No. 12 - Cast on Standard Line" in The Inland Printer, Vol. 23, No. ? (1899): 223.
By at least the circa 1939 Specimen Book of Linotype Faces (aka "Big Red") - but I suspect actually much earlier - the Mergenthaler Linotype Company was offering matrices for composing "self-spacing" typefaces for tabular work. See: "Self-Spacing Faces in Specimen Book of Linotype Faces (ca. 1939) .
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