A hat maker is also known as a hatter, a milliner or a modistep; he not only makes the hats but also sells them to other retailers. A milliner is a person who in particular makes or sells women's hats.
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A person, who makes men's hats, is usually referred to as a hatter, while one who specifically makes women's hats is referred to as a milliner. Hats are usually used for beauty, and for protection against things like the sun.
A hat maker is called a milliner. A hat maker is someone who makes and sells hats. There a number of millliners in the UK who make hats.