How does luminosity differ from the brightness of the same object as seen at the earth?
Luminosity is the "wattage" of the light. Brightness is how that object appears to an observer on Earth and is influenced by a few factors.
There are two things that affect how the light of an object is seen from Earth: the luminosity of the object, and the distance from Earth (there is an associated third thing which is the dust and gas the light passes through, but I'm going to ignore that for this answer).
Think of it this way - luminosity is like the wattage of a light-bulb. There are bright bulbs and not so bright bulbs but those bulbs that are of equal luminosity and at equal distance to the Earth should appear to be equally bright.
But if a bulb is much farther away, it will appear dimmer than one that is much closer. And, in fact, because light disperses as a function of distance squared, a bulb that is dimmer but closer can appear to be much brighter than one that is more luminous but farther away.