Definition
The magnitude scale dates to Hipparchus. Modern apparent magnitude m is defined so that a difference of 1 mag corresponds to a flux ratio of 2.512 (the fifth root of 100). Vega is roughly m = 0; the Sun m ≈ −26.7; naked-eye limit about m = +6.
Absolute magnitude
Absolute magnitude M is the apparent magnitude an object would have at 10 parsecs. It allows comparing intrinsic luminosities: M = m − 5 log₁₀(d/10 pc).