If you go somewhere where vegetarians are not common (ie. rural Portugal), the common understanding is that vegetarians do not eat meat or fish. While this is true, it’s an oversimplification. This leads to the misunderstanding where chicken stock in soup is suitable for vegetarians because there is no meat in it (my grandma nearly did this, until I asked what kind of stock she uses).
It’s not too surprising as people follow vegetarianism to varying degrees. Some people eat eggs and drink milk, some don’t eat eggs, some don’t drink milk but eat eggs. So they can say “I am vegetarian, but I don’t eat eggs”. And there is some people who say “I am vegetarian, but I eat fish” because they don’t know what a pescatarian is and further cause confusion.
There is even one vegan that eats oysters because reasons. Some people are strict and others are lax, and others make stuff up as they go along. Partly this is due to people’s motivations for becoming vegetarian, I think the other part is ignorance (see “no meat and fish” from above).
So what is a vegetarian? When I started being more strict and doing more research, I found the UK Vegetarian society to be a good source of informationa. They define a vegetarian as someone who:
“…lives on a diet of grains, pulses, nuts, seeds, vegetables and fruits with, or without, the use of dairy products and eggs. A vegetarian does not eat any meat, poultry, game, fish, shellfish* or by-products of slaughter.”
I think this is a pretty good definition. If explaining what a vegetarian is to someone, I would even just use the last sentence despite it’s limitations (where do insects fit into this?)
Though I understand that even with a more consistent understanding of what it is, there will always be diversity in practice - and that’s okay too!