Why is the territory containing rome called the papal states?

Because once upon a timeit was the POPE who controlled a large swath of powerlike a KING, which included large territories.

But over the years, and power shifts laterthe Pope became less and less important, and more or less became boxed in, within Vatican Cityhis last seat of Power. When Italy became a Unified Countrythey had to arrange a special deal with the POPE that left him in charge of his little areaa King, of sorts, within the Kings Kingdom. So they declared his little Popedomseperate , and allowed him to keep his little seat of Power.

Because broadest terms allows the law flexibility depending on changing society and circumstances.