True origin of the term "Spline" In mathematical contexts the term spline essentially refers to interpolating or approximating piecewise functions with continuity constraints.
According to the history of mathematical splines

In the foreword to (Bartels et al., 1987), Robin Forrest describes "lofting", a technique used in the British aircraft industry during World War II to construct templates for airplanes by passing thin wooden strips (called "splines") through points laid out on the floor of a large design loft, a technique borrowed from ship-hull design. used in aircraft design

and also remarks that

The word "spline" was originally an East Anglian dialect word.


Today however I came across a different meaning of the term "spline" in an article headlined Design parameters for spline connections:

Splines are machine elements that connect a shaft with a rotor.

That leads to further questions regarding the "genealogy" of the term "spline" that is nowadays used in the context of piecewise functions:

*

*Are the "wooden-strip splines" named after the "shaft-connection splines", or is the equality of the term "spline" in these cases a mere coincidence?


*A more linguistic question: is the word "spline" a true dialect word that corresponds to a different "official" word, or is it rather a proper English word that was in broader use locally, maybe because of a higher concentration of machines, resp. machine-design activities?
 A: The Oxford English Dictionary doesn't necessarily give the earliest uses of a word.  But spline with the meaning "A long, narrow, and relatively thin piece or strip of wood, metal, etc.; a slat." is quoted from 1756, much earlier than "flexible strip of wood or hard rubber used by draftsmen in laying out broad sweeping curves" (1891) and "A rectangular key fitting into grooves in a shaft and wheel or other attachment so as to allow longitudinal movement of the latter." (1864)
OED says "Originally East Anglian dialect: perhaps for splind (compare older Danish splind , North Frisian splinj) and related to splinder", where "splinder" is a splinter with uses noted as early as c1440: "Þe splyndre or speele þerof schal entre into hys hoond".
In the Philosophical Transactions of the Royal Society of 1803 I found: "This word is, perhaps, not universally understood: it is the technical translation of the French cheville. When there is a gap, chink, or rift, in the wainscot, which a carpenter is employed to fill up, he cuts a lath to the length of the aperture, planes it to the right width, and inserts it. Such inserted bits of wood, contrived to fit a given vacancy, are called splines, or chevilles...
