The Vega system or Johnson system of magnitude sets the zero point for magnitudes, basically using the magnitude of the star Vega as zero. This is used for a general (visible light) magnitude, bolometric magnitude, and for magnitudes associate with individual bands of photometric systems, i.e., a star's B-magnitude would be zero if it matches the b-magnitude of Vega. Though the Vega system's principle is "Vega's magnitude is zero", in fact, absolute brightnesses have been adopted for the system that only approximate Vega's current magnitudes.
A consequence of magnitudes being logarithmic is no magnitude cannot represent "zero flux" since zero has no logarithm (or it might be referred to as "minus infinity"). A brightness must be chosen to be represented by zero magnitude, which defines the magnitude's scale.
The Vega system can be thought of as part of (or the same thing as) the UBV photometric system.
Other systems include the AB system, which makes no pretense of matching any particular star.