Bond is usually lightweight and smooth, and is used for copy machine, laser printing and typing. Some bond used for stationery is quite elegant with a high rag content and watermarks. Color printer paper is also of better quality, with a surface that is less likely to bleed through with ink jet printing. Cover is heavy weight used for booklet covers, folders and cards. It can have any surface texture and often is made to match a line of quality text and envelopes.
Duplex cover is two sheets of quality text laminated together, usually two colors.
It can be quite good for artwork and book arts because of the stiffness and the design options offered by the two colors. Sized means there is some gelatin or polymer applied to the paper surface or into the pulp to make the paper stronger and less likely to soak up moisture. Pulp is the material paper is made from. Wood chips are cooked in acid to break up the fibers. Residual acid can react with things in the air and make paper weak over time.