Was the Forbidden City Called a "Within City"? No—It Was the Imperial City

No. During the Ming and Qing dynasties, it was officially the Imperial City (皇城, Huángchéng) or Purple Forbidden City (紫禁城, Zǐjìnchéng)—"Purple" referencing the North Star (celestial emperor's seat), "Forbidden" denoting restricted access.

"Within city" is not a historical term for it.