I definitely mean "beige box." Red boxes were (mainly?) for telephone company phones that would recognize the coin tones. Those phones had a different line "class of service" at the switch end and the critical point is that red-boxing was the only way (post blue-box era anyway) to get free calls off of them. Well, at least that I knew of. But a COCOT had all the "pay phone magic" embedded in the phone itself - the line was a normal line, so if you clipped in at the demarc box, "upstream" of the actual phone, you were on a plain old phone line (with long-distance service) that you could use to your heart's content. And by the time frame I'm talking about, there weren't a lot of the red-box'able telephone company payphones around in our area.

If some COCOT's were also susceptible to red-boxing, that's something we never discovered. To be fair though, it never even occurred to me to check. I just had it burned into my brain at some point that red-boxing was for telco phones and not COCOT's.[1] In hindsight, that was quite possibly folklore that was wrong.

You could ofcourse use it on a COCOT, but you could also use it on any telephone line.

Yep. It just worked out that a convenience store in the middle of nowhere with a COCOT out in the parking lot was a good scenario for doing this kind of thing without getting caught. Or so I'm told... :-)

[1]: https://www.tech-faq.com/red-box.html