A unitard is a skin-tight 1-piece garment with long legs and,
sometimes, long sleeves, whereas a leotard is a similar garment
which does not have long legs.
To put it simply, a unitard is a combination of a leotard and
tights, all in one layer.
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this garment which you are talking about is known as a 'leotard'
as Mr. Charles Leotard invented them.