Blunt wraps arn't cigars, they are a cigar like paper usually flavored.
There are a few main parts of a blunt:
1) Leaf: This is the outer part of a cigar you will normally see

2) Paper: I have NO clue what this is made out of, but its normally a brown paper right beneath the leaf and you'll be able to see a line going down the center of it to the very tip. This is where you should crack the blunt, or where I crack it.

3) Cancer Paper: This is a gray peice of paper around the mouthpiece of the paper (not the leaf). I have no clue if it really does give more cancer or whatever, but thats the common name for it around here. I always take it off.

4) Tobacco, aka guts: I've found pieces of metal, woodchips, plastic, sticky white stuff, sticky black stuff, pieces of paper, and many other things which are definatly not good for you to smoke inside of it.

I normally remove the leaf from the cigar so after i roll it up (doesnt matter how tight), i'll have the leaf to tighten it up, add flavor, and shape better with.