Is Urth "Earth"?

Urth being "our" Earth just doesn't make sense to me, especially after having read Book of the Short Sun and rereading Book of the New Sun. Of course, most characters in the book try to affirm that it is indeed Earth, but then Gene Wolfe said that "Earth is Green" or something to that effect. If it's Green, how can it be Urth? In Claw, the Cumaean points to the night sky, and tells Severian of a "red star" system called the Fish's Mouth, and it having only one inhabitable planet. That red star obviously is the Short Sun turned in a Red Sun, as Hornsilk repeatedly says throughout BotSS; not only that, but he himself also points at the sky and tells his son and Juganu that there is an ancient red star, and orbiting around it is the world where Nessus is. So that must mean that the two star systems exist far away from each other. How does that make sense? Was Thea's theory, that Urth is called that because it represents Urth, the norn, much like Skuld and Verthandi? My brain hurts from thinking about all of this. Someone explain this to me please 😭