Vegan and vegetarian are different.

Vegetarian is related to religious belief (like sects of Buddhism or Hinduism) while vegan is related to animal rights movement. Hence vegetarian can drink cow's milk, while vega do not consume dairy products.

The food type is also different. Vegetarian tends to eat food of their religious culture (indian vegetarian food for hinduism, Chinese vegetarian food for Buddhism), while vegan have food that has modern counterparts like vegan spaghetti or oat milk.

For Chinese vegetarian, they also eat beancurd and tofu that resembles animal (like tofu-chicken) but this could be offensive to both vegan and hindu vegetarian

- my note as a Malaysian