The term midget is different from dwarf based on body proportions. A person with dwarfism has disproportionately short limbs. The term midget was used to describe persons of small size but with normal proportions when compared to average people.
The word dwarf is not considered offensive. The word "midget" is considered offensive for either description. It is considered most offensive when misused to describe those with dwarfism. The term "homunculus" may be less offensive.
Differences in associated problems
While there are many problems associated with Dwarfism, midgets are not plagued by these problems. Midgets are just normal people whose height is stunted. In the case of dwarfs, the physical conditions affecting them are: malformed bones, nerve compression, joint disease, and disoriented growth of some organs.
Both midgets and dwarfs have to suffer the psychological or social problems associated with their condition. Social prejudice against their extreme height may reduce their social confidence and opportunities. Sometimes they're mocked and may suffer from low self esteem. Sometimes extreme shortness (height of less than 3 feet) may interfere with their day to day chores.