I found my love of drawing when I was about 15. Which means I've been accumulating a collection of drawing pencils and other supplies for 13 years. I ran around my house, gathering up all the drawing pencils I could find, so everything I've made for this is based on my current hoard. I promise to come back and update these charts when I have access to what's missing, but this should answer many of your questions.
Let's start with the basics; what is a pencil made of?
Most people, when they think of a pencil, imagine something like this:
A yellow number 2 pencil that we all used in school to fill in a scantron or do math homework.
Part 1: Anatomy of a Pencil
The tip of the pencil (sometimes called the pencil lead) isn't actually made out of lead (Pb) at all. It's a combination of graphite and clay. Graphite is what actually leaves the marks on the paper, and clay is what keeps it together.
Varying proportions of graphite and clay are what cause the different grades of pencils.
A larger proportion of clay creates a harder tip and leaves less graphite on the page, creating lighter lines. The less clay used, the softer the tip, leaving more graphite and darker lines. (This also means that the pencils wear down much more quickly and need to be sharpened more often to keep the tip pointy.)
While art supply companies all have different ideas of what grades of pencils belong in a set, they all use the same grading system. A #2 pencil, also known as an HB pencil, falls in the middle and is included in every set I've ever seen.
(these are the examples on the pencils I have on hand)
Traditionally, pencils have a wooden casing made from cedar. This helps prevent you from getting graphite all over your hands and increases their durability.
There is such a thing as woodless pencils or woodless graphite sticks. They are great if you are someone that likes to shade with the side of your pencil, but a word of caution: without the wood casing, these pencils are much more fragile. If you're like me (clumsy), plan to travel with your supplies, or have a firm grip, these things will snap in half.
Unlike normal #2 pencils, drawing pencils usually do not have attached erasers
but, most pencil sets come with an eraser.