Sir John,
recalcitrant !- well u codger you.... LOL ,,,,, OK lets settle this geodesic versus geodetic once and for all. They are usage-specific, application specific if you prefer. One may say the geodetic is the nature of the beast, the type of survey, or as you showed - the type of structural modus; highly application and field specific.
Geodesic is the beasty itself, the shape of the spherical,spheroidal, hyperbolic,or otherwise an arc, catenary etc sometimes in sag engineering, varying radii in geodetic surveying along a geodesic great circle arc due to the oblate earth spheroid with gravity ever-changing, - subject to isostasic deflection of the vertical and the variances of the geoid - the spheroidetic, undulating surface of gravimetric equipotential, viewed as sea-level at rest.
Which is what various datum i.e. NAD83 have their reference tri-axial ellipsoids derived from. For final field-specific vernacular - read National Geodetic Surveys Book - called a professional paper by them - called - "The Geodetic Glossary" - It is written by PhD Geodesists our nation deems experts. In it you will find both definitions, as they apply to Geodesy and geodetic surveying, datum, and map projections.
One may find variations in usage of the terms in varius fields, geodesic is more common in my experience in other fields; notably engineering, but I will not debate your field John. In mine, the parlance is shop, of common usage, and in the books - after all this time if you don't trust me, order the Geodetic Glossary. Or borrow it from the library, or read some references on the internet - National Geodetic Survey, formerly The U.S. Coast and Geodetic Survey, still a branch of NOAA.
I really don't mind if you disagree - it is inconsequential in the long run. I wished to share with you over the past, and one more time here, the field-specific parlance that will vary wherever you look in different app's.
Your time would be more enjoyably spent not attempting to prove me wrong !

All in good friendship John, you know I have great respect for you. I don't know why you doubt me so in my own field and seem obsessed with proving me wrong, even in my absence, on one TERM.
Good God man ! Temperance ! LOL OK ok LETS LET IT REST EH ? I am quite sure the other readers think none the higher of us for bantering on this, and aren't the least interested. We can I'M each other on it if you like. I grow weary though, and far more important things on my mind - like how to... welll, nevermind. Safe to say I am consumed currently.
"We traverse in lat-lon along geodesic great-circle arcs in geodetic surveying" - utilizing the geodetic-forward formulae. The French Canadians, and Canadians in general - where GIS is called Geomatics in University curriculum - world-renowned mappers - and Royally Chartered Surveyors - are called "Geodesiques", that do geodetic work. OK OK ok ? lol good to banter with you again, John.
BTW - I will not take advantage of your social gaff about me not returning the phone call - I had to have Merry taken by ambulance down to the hospital, where she was in intensive care for a month. I was a bit busy...
And I'll spare you the hardest news here, I do not wish to embarrass you or make you feel bad. Please see my 7/10 thread "Hello Geodeticman aka geo Steve is back" - and you'll see where it all led, to my deep sadness. I'd still enjoy talking directly to you some time, and we can talk shop. Perhaps we can avoid snoozing the rest of members in general forum by IM'ing on such minor things as proper technical usage of terms in MY field. LOL OK Sir John ?
Respectfully,
geo ..er.. recalcitrant Steve