The designations were given to spectral lines in various alkali metals, which were grouped into series. At the time shapes of orbitals were not known - orbitals and their connection to spectroscopic transitions were discovered later. As you might guess, lines in the sharp series were, well, sharp peaks, whereas those in the diffuse series had a lot of fine structure. These two designations came from emission spectra, primarily (I believe) sodium, which was one of the first studied. https://en.wikipedia.org/wiki/Sharp_serieshttps://en.wikipedia.org/wiki/Diffuse_series
The "Principal" in principal series derives from similarity(in pattern) of absorption lines of alkalis to those of corresponding hydrogen spectra (for obvious reasons, as we now know), against which many atomic spectra were usually compared as a benchmark. Since the hydrogen spectra were the ones that were first seriously analyzed, their spectral line series was known the best - so I guess the "principal" appellation for similar spectral series that appeared in the alkalis makes sense.
I'm wasn't sure where the fundamental comes from, but according to this:https://en.wikipedia.org/wiki/Fundamental_series
It seems like it was because the discoverer thought the line pattern was much simpler than other series, perhaps because the fine structure was too small to be easily observed.
Anyway, eventually the origin of spectral lines was discovered as quantum mechanics was formulated (actually, coming up with ways to explain the spectral line patterns was a big part of that), and the orbital transitions that gave rise to the spectral lines took the names of those series....and the rest is history.