According to Laport, who Cebik cites for accuracy, the Counterpoise was a network of conductive materials disconnected from the earth that was limited in its distance from the actual earth to the point that it provided capacitance between the network and real earth. This would enhance the performance of antennas particularly over poor earth/soils. It is coincidental that it may bear resemblance to a groundplane set of radials.
The article takes some pains to differentiate between a counterpoise, which is not the other half of the antenna, it would seem, and a set of GP radials, which are the other half of the antenna. Additionally, Cebik seems to make the case for the counterpoise being non-existent once the antenna exceeds the point above the real earth (based on wavelength of operation) that capacitance can no longer be formed between the earth and the radials/mesh network. and he clarifies that ground contact radials, or buried, are not a counterpoise because capacitance cannot be formed to the point a true counterpoise does being isolated from earth and near enough to act as a large air capacitor.
Throughout the article he attempts to follow the trail of time over which prominent writings and general usage of the term led to an obscuration of the historical and true meaning of the two terms. His conclusion at the end of the article is that considering it will be unlikely that operators and educators will be willing to accept the reintroduction of the true historical meaning/usage of counterpoise the best solution may be to eradicate the term from antenna parlance completely.
I am not surprised by the current use of the word (which I also have done) as an exchangeable term with Goundplane, but apparently in its original truer usage it was not interchangeable at all.
That's how I read it.
Perhaps the nearest thing I see in current use of the concept is the mobile installation. Looking at it I believe I see the automobile acting as a counterpoise to the earth, the earth being the true groundplane. I find this outlook potentially sustainable due to a phenomenon all have experienced when moving an antenna from the fender or trunk, which placed the nearness of the earth closer to the 1/4 wave radiator, to the roof of the automobile. which put it farther from earth, or vice versa. SWR changed, and we sometimes struggled to recover a good match.
I believe this may be due to the alteration of the capacitance between the vertical in relationship to the distance of the insulated counterpoise of the automobile from the earth (the tires). Many have owed this SWR change to creating or removing reflection due to metallic parts of the vehicle, and in some cases this can be true, but there may be more to the story.
My thoughts . . .
I am not the teacher here, but one of those unwilling to learn my subject wrongly.