I am fairly certain that they use the same console system. For instance, right-clicking on the title bar gives the exact same options as in `cmd.exe`. I was perhaps a little overzealous in calling it cmd-based; that's a slip-up on my part simply because `cmd.exe` was the only program to use that system before. Thanks for keeping me honest.
Both use the Windows console host, effectively what a terminal emulator is on Unix-likes. It provides the window and a bunch of other functionality (character grid with attributes, history, aliases, selection, drag&drop of files into the window, etc.).
It's just that every console application on Windows uses that host. This includes cmd, PowerShell, Far Manager, or even vi. Sorry, I may have seen it conflated with cmd too often. It just nags me. For Linux users it's probably when everyone starts calling a terminal (emulator) "bash".