Actually, a midget is a person of normal arm/leg ratio: like a human but smaller. Often due to pituitary problems. I've never seen a case (they usually are treated with growth hormone injections nowadays).
Dwarves are usually with shortened limbs. The most common is the achondroplastic dwarf, who has typical features that make them look alike. But there are several other types of dwarfism too.
There are a lot of medical problems that they face: one of my patients had a baby with achondroplasia who needed neurosurgery early in life. And the Little People of America website has lots of help for parents.
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Now the ALIEN lobby will be on your case!