This case study examines a Schwarzschild black hole through three theoretical descriptions: geometric (general relativity), thermal (Hawking temperature), and entropic (Bekenstein–Hawking entropy). All representations refer to the same physical state and are evaluated under identical SI-defined parameters. The analysis quantifies differences in how each theoretical framework organizes scale relations when projected against a fixed Planck-referenced basis. Pairwise structural differences are computed across three temperature regimes (3 K, 300 K, 3000 K). The results show a stable ordering of representation distances across scales and reveal consistent separation between geometric and entropic descriptions. No modification of the underlying physical theories is introduced. The study measures structural organization only.