“There’s a long history of hard tops without B pillars also being called hardtop convertibles by GM.
The 1972 Buick pictured in post #4 was referred to as a hard top convertible by GM. My parents had a similar Chevy at that time.”
If there were a long history, It would be documented.
I am 78. On a convertible the top retracts.
I'm not that old. But in 1962, when I was a little kid, my Dad brought home a new car. He said it was a "hard top convertible". And he said to "go outside and take a look". So I ran outside expecting to see a convertible and instead I saw this.

And now for the history lesson.
It's as I said.
Where were you in '62?