Dander is what bodies of pets shed, including fur, hair, and feathers. That can be a cat, dog, or other pets. It’s comparable to dandruff, where an excess of flakes becomes visible.
As for dust mites, they’re incredibly minute bugs, classified as spiders. They thrive in home dust off the dead skin that people shed. Breathing the waste product of dust mite can trigger your immune system to combat a harmless substance, thus causing sneezing and a runny nose.