Luminosity
Luminosity is a measure of the total energy given output by a star at all wavelengths from gamma radiation to radio waves.
The luminosity of a star depends on:
(a) the size of the star
(b) the temperature of the star

Brightness
The brightness is how bright a star appears when seen from the Earth. The brightness of a star depends on:
(a) the actual luminosity of the star
(b) the distance of the star from the observer on the Earth
If we have two stars of the same luminosity with one star double the distance of the other from the Earth the closer star will look four times brighter.