First, paper is made from fibers.  Some are wood pulp, some cotton, some plant fibers like hemp, linen (flax) or other bast fibers of plants.  A bast fiber is the inner layer of the bark... and the most famous is mulberry fiber which many mis-name rice paper fiber because it is from the east. 

Second, paper is made with hydrostatic bonding through the pressing of wet hydro-pulped fibers into sheets.  This means the bonding depends on weight, pressure and chemstry additives.  To secure the bond, sizing is added to the mix.  This is called internal sizing.  Most (not all) paper has internal sizing to handle ink and light water from pens and media. 

Heavily internally sized paper is for printmaking so it can be soaked in water and then printed on using various methods.  Lightly internally sized paper is for very light watery techniques.  Most eastern papers are lightly sized.  The less sizing internally the more inks will bleed in the paper.  And no sizing is basically a blotter paper.

Externally sized paper is paper with an additional coating on it to stiffen the fibers on the surface and resist water.  Gelitan sizing is used for watercolor paper and creates a boundary to the paper so the water dries more on the surface.  The mediums used will also dry mostly on the surface.  These papers are also good for acrylic painting.

Almost all quality paper is PH neutral.  Meaning it has no acidic content. Base PH chemicals are used to whiten paper but can attract acid to the fibers over time which breaks down the paper from within.   Acidic papers yellow quickly.   PH neutral paper is archival quality and last for a long time depending on what medium is used on the surface. This stays white for a long time and slowly tans (tanins in the air)... The oldest paper is about 700 years at this point.  Paper made in the rennaissance is of greater quality due to the environment than today where acidic air is constantly present during the process of making it.

Paper often has direction.  This means that the machine or roll is created in a specific direction and will fold easily in the same direction as the curve of the roll or 90' to the direction of the length.  It will also tear more easily in the direction of the length of the roll because the fibers are lined up along that direction.  Tear a newspaper in either direction.  One way it will tear straight, the other it will curve off in a direction.  This is true for machine made quality papers. 

The best papers are mold made or hand made.  Mold made is a machine process but the fiber is shaken in both directions before pressing so it has no direction.  Hand made is too and is much more expensive due to the labor involved.  The higher the quality of paper the better the results with the medium that is being used.

Weight of paper is determined by how much fiber content exists in a ream of paper of a standard size - often 22x30 is considered a standard size.  But there are different standards for European, American and Asian papers.  So the weight can be confusing.  LBS or GSM is for pounds and grams per square meter respectively.  The higher the number the thicker the single sheet of paper is. 

Tooth refers to the surface of the paper.  High tooth has a lot of bumps in it and is good to grab charcoal, pastels and pencils.  Low tooth or smooth is for ink and pen uses.  Plate tooth is for markers and manga style and has a very hard surface.

Temperature is the relitive temperature of the drying roll or press as the paper is made.  Cold Pressed paper is most hand made paper and is a standard paper for almost all uses.  Hot Press paper is when the water is also driven out of the paper through heating.  This leaves small holes or vacuums where the water boiled away.  Thus the paper is "softer" and more "open" to absorption of water or fluids later.  Rough is often used to indicate a middle ground between cold which is harder paper than hot which is soft.

Specific Papers

Newsprint Paper - this is a cheap recycled paper and is loaded with acidic content from the chemicals used to rebreak the bonds and reseal the bonds in making it.  It is good for quick non-perminent sketches.  Most Newsprint is from 18-25 lbs or lighter.  Rough and smooth are the two general surfaces.  Rough is needed for charcoal because it has tooth.

Sketching paper - almost all of this type is wood and cotton fiber paper made by machine and cut with a specific direction.  Often this paper is light in weight being between 50 lbs and 65 lbs.  20 lbs paper is copier paper.  So it is a little more than 2 times heavier.  If sketch books are left in the sun they will bend to the oposite direction of the paper. 

Drawing Papers - the biggest difference between drawing books and sketching books is the weight of the paper.  Drawing paper starts at 70-80 lbs and goes up from there.  Average is 85 lbs.  This is not to say that heavier paper cannot be found - 140 lbs is a popular drawing paper.  In a book these papers last longer and hold up to more media than just pencil. 

Print Making Papers - This paper is heavily internally sized and natural or cotton fiber paper.  It can comes in 90-300 or more lbs depending on the needs of the artist.  The artist will wet the paper or use a heavily wet thick ink to impress on the paper.  Thus internal sizing keeps the paper from curling and buckling.  BFK, HW & LW, Arches Cover, Silk Screen are papers which are for print making. 

Watercolor and Painting Papers - Watercolor has external sizing as well as internal and often it is gel sizing.  This paper is heavier or stiffer by nature.  The paper can come in books, blocks or single sheets.  140 lbs is often the lower end of the watercolor range, though 90 lbs is available and good for book work.  300 lbs keeps it shape under a wide range of very wet techniques so is better for acrylic painting.  200 lb w/c paper is great for a coat of gesso for painting with acrylic or oils.

Charcoal Paper comes in a wide variety of color is generally 90 lbs and has a tooth to grab the medium.

Card Stock has a plate finish or hard surface and inclusions of clay to maintain its hard surface.

Vellum is a hold over term from natural vellum or cow or sheep hides which were very thin and translucent as is the term Parchment.  This is often 16-25 lbs paper good for drafting or sketching.

Tracing Paper or rolls is very light 12-16 lbs and often has little or no sizing so can only be used with light inks or pencil.

Bristol Board or Vellum is a heavy plated (clay inclusion) paper which holds up to a lot of mediums including inks, paint, markers and the like.  This paper is defined by "ply" meaning several layers are bonded together at the last point of drying.  2-5 ply paper becomes more and more like stiff board.

Illustration Boards and Presentation Boards can be found with surfaces that are cold or hot pressed.  They have a base structure and a cover layer of paper similar to what is described above.

Mylar is not paper but rather plastic sheets.  With a mat side (SM) or double mat(DM) sides, this surface allows for drawing because it has tooth to catch the pencil or charcoal medium.  Mylar is becoming more and more rare with the use of computer graphics.  003ML (the thickness) is the easiest and most available to find.

Mat Board comes in a wide variety of colors to frame out or mount artwork on it.  Any mat board with a white core is most often acid free and will not damage artwork.  But beware!  If it is not specific about its acid content, then beware the degredation.  All museums consider black on black mat board to be acidic even if it notes that it is not.  Black pigment is highly attractive to acids in the air and thus museums will reframe work to white mats for preservation.

Foam Board is acid free, comes in a variety of thicknesses. It is plate finished (having clay) and is most often acid free.  This is the best board to mount artwork to.

Cardboard is not and never will be acid free.  It is recylcled like most newsprint and due to the chemestry of the glues and the like, will ultimately damage anything that is mounted to it with acidic breakdown.

Choosing the right paper and it will give the best results as well as preserving ones work for the long haul.  Warnings should be noted.... Andy Warhol's work was often on anything he could find... this was great for a quick print and getting loads out to the world... but the price paid then is a price paid now.  Many of his prints are disintegrating after 40 years because of the acid content of the paper. It is destroying the structure of the work!  Choose wisely!