Sure. Usually it boils down to whether fish/seafood is considered vegetarian, but sometimes it also includes broth or animal byproducts.
For the purposes of definition, I use the below, which appears to be the general consensus definitions in America, though I'm sure some will dispute this.
Vegetarian: (also called ovo-lacto vegetarian) No meat (including fish/seafood). Eggs, dairy, and honey are okay. Byproducts that involved killing animals are not. Those vegetarians that are so for health reasons often skip that last part, and many vegetarians only go "so deep" when looking, so they don't worry if bleached (with animal bone) flour was used, or if the cheese was made with animal-based rennet. Lastly, insects and some low-nervous system mussels occupy a questionable space that isn't often discussed at large, but like the "so deep" issue should likely be considered "not strictly vegetarian but some vegetarians have exceptions".
Vegan: Vegetarian, plus no eggs, dairy, or honey. They tend to look deeper and more strictly than vegetarians, though the general belief that you shouldn't be killing things is shared between those vegetarians and vegans that are so for ethical reasons. (other vegan restrictions aren't food based)
Pescatarian: Vegetarian, but fish and seafood are permitted.
Some examples:
In the American southeast (not a foreign country, but might as well be) pork is as much a "spice" as a food. Many vegetable offerings at restaurants are seasoned with pork. At one cafe in Atlanta I asked if a soup was vegetarian and they said yes...then after a moment said "but it does have chicken stock", because in their mind anything that wasn't "chunks of meat" was vegetarian. (also, since I have the pulpit, as a once lover of ham, what the south does to ham is a crime. It has two varieties: salty, and really salty. I forget which is "country ham" and which is "virginia ham", but both made it easier for me to drop pork from my diet.)
In Chinese food, fish is generally considered vegetarian, and oyster sauce is particularly prevalent. If I request something "vegetarian", they'll avoid using pork-based seasonings, but will include oyster sauce unless I'm very explicit and make a pain of myself.
My Japanese friends tell me there's no point in me trying to eat there. The only option that doesn't involve seafood is "monk training food", which is...not intended to be tasty.
Thai food and Vietnamese food have, I think, some of the same issues. I know curry paste is often made with shrimp, and where an Indian restaurant will pay attention, Thai places often won't. (That said, I love Thai, so when I find a place where I trust the staff "gets it", they get a lot of business)
I wasn't vegetarian when I was in Europe, so I don't know how easy it is to be vegetarian there, but I know a lot of places that had a strong Catholic influence consider fish to be "non-meat".
In many of these places I could try to be explicit, but that's often painful because there are sometimes language issues, because I don't want to make a pain of myself, and because some places leave me not trusting that the result is actually vegetarian despite my explicitness.
In contrast, Indian restaurants tend to:
1) Share the same definition, so we have no language issues
2) Take the vegetarian/non-vegetarian divide seriously (Many Indians are vegetarian or part-time vegetarian for religious reasons), so my requests are neither a pain nor is there often a worry that I'll get something animal-based anyway.
A friend of mine from India once told me "if a mob would burn down your restaurant if you got caught mixing meat and vegetarian, you'd take it seriously too". I still don't if she was joking with me, and if so to what degree.