|I'm not sure what the difference is in your mind.
std::format (C++ 20) aren't really API's in my mind. They're fine for a simple utility (think ping or netstat), writing log files or doing data I/O, but quickly become unweildly when trying to do full screen I/O like menus, dialogs, pop-ups etc. If you're pursuing the latter, then you probably want to use a library that handles all the screen painting for you, managing overlays, pull down menus, etc. You might want to look at this page to see if any of them meet your needs C++ Library TUI libraries | LibHunt
You can probably find other examples googling for C++ TUI libraries.
Keep Calm and Carry On