What two magnitudes must be compared to calculate the distance using the difference in brightness?

Absolute magnitude and apparent magnitude

The calculation of cosmic distance using standard candles like Cepheid variables fundamentally relies on comparing two specific measures of brightness. The first is the absolute magnitude, which represents the star's true, intrinsic brightness if viewed from a standardized distance, determined via the Period-Luminosity Relationship. The second is the apparent magnitude, which is the actual brightness measured by the observer through the telescope. The disparity between the star's actual brightness (absolute) and how bright it appears (apparent) is solely a function of the distance the light has traveled, quantified through the distance modulus relationship linking this difference to the logarithm of the distance.