centerpiece (sèn´ter-pês´) noun
1. Something in a central position, especially a decorative object or arrangement placed at the center of a table.
2. The central or most important feature: "Now comes decontrol, the centerpiece of [the President's] energy program" (Tom Alexander).
Excerpted from The American Heritage® Dictionary of the English Language, Third Edition © 1996 by Houghton Mifflin Company.
Centerpiece does not mean a flower pot or a flower vase. A flower pot or a flower vase may be placed at a center of a table to serve as the main decoration, and then it will become a centerpiece.
A chest of drawers is a piece of furniture consisting of a set of drawers that fit within a frame. A chest of drawers usually contains clothes but you could put all kinds of materials in a chest of drawers such as personal items, pictures, books, documents etc.
A dresser is a low chest of drawers often supporting a mirror and typically used for holding clothes and personal items. A dresser is also a cupboard or set of shelves for dishes or kitchen utensils.
It is not the same as a dressing table. A dresser may double for use as a dressing table but it is not a dressing table.
A dressing table (sometimes called vanity) is a low table with a mirror at which one sits while applying makeup. A dressing table does not have drawers.
However, a bureau is a chest of drawers, especially a dresser for holding clothes.
Cutting board is the same as chopping board. In the west, it is a cutting board. However Chinese advertisers in Hong Kong and China often advertise “chopping board” instead of “cutting board”. Maybe the board is often used for chopping than cutting.