A rug is a piece of small carpet that doesn't cover the entire room. Some people call rugs carpets too. They often have a fringe around the edge, or a bright pattern on them. Rugs are usually bought to look good.
A sculpture is something made by people that looks interesting. Sculptures can be any size and made out of almost anything. Small sculptures are often made from clay and large ones are often made from stone or metal.
Sculptures are similar to statues, but often sculptures are abstract, which means they are interesting to look at but you can't tell what they are supposed to be, or they are deliberately made to be not an accurate copy of whatever the sculpture is supposed to be of.
A shelf is a horizontal piece of wood or metal that is attached to a wall so you can put things on it.
The plural of shelf is shelves.