Tear stains does not affect only pets with white fur, pets with black or brown coats could have tear stains too, they just appear more obvious on white fur.
Tear stains occur when your pet has excessive tearing (epiphora), and the porphyrins in the tears stain the fur a rust colour. Porphyrins contain iron, hence the rust colour. Tear stains can become brown when, due to the constant moisture, a yeast infection develops on the stained area.
Epiphora can also irritate the tear ducts causing them to become swollen, inflamed, or even clogged. You will see more mucus (or crust, when dried) around your pet’s eyes, which, if serious, could lead to eye infections.