I've been meaning to do a write-up on this, but there are really 3 different characteristics of a cigar, and people use the terms interchangeably which causes a lot of confusion.
"Flavor" -- the amount of flavor a cigar has (subtle = mild, strong = full, etc.)
"Strength" -- the amount of Nicotine content in the cigar
"Body" -- the degree to which the smoke effects your palate. Not simply "is the smoke thick or thin," but rather, how does the smoke make your palate FEEL? Is it in-your-face peppery, causing tingles everywhere? Then it's probably on the fuller end. Does your mouth feel pretty normal between puffs (flavor aside)? Then it's on the milder side. A full-bodied smoke "fatigues" your palate more.
For me personally, flavor is my #1 interest. However, if smoking on an empty stomach, strength becomes a factor. Also, if I want to smoke a 2nd cigar in the same day, then it MUST be fuller in body to my previous cigar, or my palate just won't get anything out of it.
Any combination of these 3 factors is possible in a cigar.