There are UK/US differences in these terms.
A sweater is a knitted overgarment, also called a jersey. http://www.aranknits.com/sweater%20front.jpg
A sweatshirt is a knitted informal overgarment, originally designed for use by sportsmen. It can have a hood attached, and the material is generally cotton or a cotton mix with a fleecy interior. http://www.theemployeemall.com/mtsu/...sweatshirt.jpg
Plush is a form of velvet and is usually used for upholstery and curtains. Sweatshirts can be made of polar fleece, which is a synthetic fabric with an absorbent pile.
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