The center of a pencil used in school is graphite, mistakenly called lead. These pencils can be used for basic drawing because the graphite in them is similar to art pencils. To create subtle effects, you might want one of the variations of graphite pencil cores. These include ebony pencils with a dark color and water-soluble graphite cores for adding to watercolors. Carbon pencil cores are dark black and similar to charcoal pencil cores. Charcoal pencil cores are also available. Technically, all three of these pencil cores are forms of carbon.
You can likely spot the differences between a drawing done with graphite and one with carbon. The graphite drawing will be light gray with a reflective sheen, due to the properties of graphite. Carbon drawings have rich black lines and might have smudge marks because carbon easily smears.
There is a reason graphite is the core of choice for school pencils. It can be erased while carbon cannot. Rubbing your hand over a graphite drawing will not run the lines as much as it would with a carbon drawing. Carbon easily smears on the page. Some artists use this to their advantage.
Graphite pencils effortlessly glide across a page because this substance has lubricative properties -- locksmiths use graphite to free stuck locks. Carbon pencils do not have this same ease of use, and the texture of a carbon pencil feels softer than a graphite pencil. The softer a pencil is, the darker the mark is makes, but the more often you need to stop to sharpen it back to a point.