Question

Why is the blood that flows from the lungs toward the heart a brighter red than the blood that flows the other direction?

Answer 1

the presence of oxygen-bound hemoglobin that makes it bright and red.

Answer 2

In lungs, the oxygen binding pigment "Hemoglobin" binds with oxygen that makes Oxyhemoglobin which is bright red in color. So when it flows toward the heart it's bright red.
Normally hemoglobin is purple or dark purple in appearance.