While there is no "proper" dictionary of furniture terms I would recommend to anyone the 10 volume collection of American Antiques of the Israel Sack Collection. Volume 4 happens to be on my desk this morning and you can easily see examples of columns, described as simply "fluted " and the flutes always stop above the base and below the capital, and yes, you do have to "carve" the very terminal end of the flute- but it really only takes a quick swipe with the proper gouge. Also in Volume 4, you can see examples of Massachusetts tall clocks with brass stop-fluted columns, and described as such in at least one example.
Before these volumes were published, Nuttings Furniture Treasury(which contained three or four volumes, I fail to recall) would have probably been the closest one would have had for a furniture "dictionary". I am fairly certain that the final volume contains Nuttings scale drawings of a Willard tall clock with the brass stop-fluted columns, and that they are described as such on his plans.
I seem to remember that there are at least a few known errors in descriptions in the Nutting work, and for this reason the 10 volumes of the Sack collection are, in my opinion, probably the best reference anywhere. While some might find fault with the fact that Sack's family was making a profit buying and promoting this furniture for sale, I would say that the descriptions and insights on proportion, beauty, and attention to detail make this the ultimate resource for the period furnituremaker. If Sack and later his sons and following generations had not truly loved and promoted this art, we would all be poorer.
I do think that reed and fluted is a fair description of these columns, but I believe that term is more typically associated with bed descriptions.
I apologize for not remembering to photograph a stop-fluted column last nite. I will try again tomorrow. If you look at the columns on my Frothingham chest-on-chest posted in the member gallery, you can see ordinary "fluted" columns, as Sack describes in Volume 4. There are two similar chest-on-chests by Fropthingham in Volume 4 that I used as reference to build this in 1989. I would not be surprised if these are not very similar(although not stop-fluted) to the columns on the desk you describe, ghuff. These flutes do stop between the base and plinth- as photographed in Sack. I really cannot recall an occurence of the flutes extending all the way to base and capital with no little "carved" terminus on a truly fine piece of furniture. I wonder how Sack might have described it.