What is the term for a star's brightness as seen from Earth?

Apparent magnitude, and the scale is a two-thousand-year-old inheritance that nobody has dared replace. Hipparchus sorted visible stars into six classes with the brightest as first magnitude, and the system was later formalised - which means it runs backwards, with smaller numbers meaning brighter, and it is logarithmic, because human perception is.

Formalising it forced negative numbers on the scale. Once magnitude 1 was pinned down mathematically, several objects turned out to be brighter than that: Sirius is -1.46, Venus reaches about -4.6, the full Moon is -12.7 and the Sun is -26.7. Each step of one magnitude is a factor of about 2.5 in brightness, and five steps is exactly a factor of 100 - which was chosen to fit the old classes rather than derived.

Apparent magnitude also says nothing about the star itself. It mixes true luminosity with distance, so a dim nearby star and a brilliant distant one can look identical. Absolute magnitude is the correction - what the star would look like from a standard distance - and getting from one to the other requires knowing how far away it is, which is the hardest measurement in astronomy and the reason Cepheid variables mattered so much.