Vegetarian means no animal product such as flesh , skin, etc.
Vegan means no animal product or by-product such as flesh, skin, milk bees wax, eggs, silk, urine, etc.
A vegan doesn't want any living creature harmed or exploited regardless of classification.
Bee's wax & honey seem innocent enough but isn't. 95% of honey is havested very harshly. The farmers steal all the honey & replace it with sugar water. The bee's eat/live off the sugar water all season rather than the honey & in the winters the farmers burn the hives & the beees inside so they can start again.
Small local bee keepers generally don't do this, but the big boys certainly do.
I was told with Vegan, even silk counts as "animal" because silk worms make it...
I watched a program on public television about silk worms. In the show the worms were boiled alive during the silk extraction process.
