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?