There are different definitions of vegan, too (most vegans use one definition, but non-vegans tend to understand better if all the variants get lumped together):
vegan (to vegans): a person who uses no animal products that they can realistically avoid, from food to clothes to medications. There are frequent fights in some vegan circles about "how" vegan someone is and if it counts (for example, people who continue to wear leather products they bought before they went vegan or who take medications with gelatin).
dietary vegan (to nonvegans, often lumped as a plain vegan): someone who avoids eating all animal products. Most of the wiggle room here does seem to be for honey, but the serious vegans frequently call these people "strict vegetarians."
I personally think there should be more gradations or terms because there are people all across the spectrum and it's hard for those of us who aren't exact to explain where we are. I eat fish once a month and still wear wool and leather shoes. If I say I'm vegan in the presence of a vegan, all hell breaks loose. If I don't say I'm vegan, I inevitably get served meat and dairy. It's all very interesting and complex.