How does luminosity differ from the brightness of the same object as seen at the earth?

The luminosity of an object and its distance from Earth are the two factors that determine how that object's light is perceived from Earth; a third factor is the dust and gas that the light travels through, but I won't address that in this response.

Consider this: luminosity is comparable to a light bulb's wattage. While some light bulbs are brighter than others, all light bulbs with the same luminosity and distance from the Earth should appear to be equally bright.

On the other hand, light disperses as a function of distance squared, so a bulb that is closer can appear much brighter than one that is more luminous, but if the bulb is much farther away, it will appear dimmer than one that is much closer.

While brightness is the perceived intensity of light received from an object as observed from a specific location, such as Earth, luminosity is the total amount of energy radiated by an object per unit of time; luminosity is an intrinsic property of the object, independent of its distance from the observer, whereas brightness depends on both the object's luminosity and its distance from the observer.