Vegetarians who eat fish are called "pescetarian". Its not truly vegetarian, its just easier to call it that. I grew up pescetarian because my family was 7th Day Adventist, and most 7th days are pescetarian (because Jesus ate fish, it must be okay). People are pescetarian not really so much for animal welfare like some vegans/vegetarians are, but for health reasons -- red meat can be bad for you, fattening, etc. while fish is generally good for you (just find low mercury fish).
When people say "vegetarian (w/o fish)" most people are talking about lacto-ovo vegetarian, which are those who abstain from meat and fish, but will eat eggs and dairy. Vegans are those who abstain from dairy as well.
You should ask if she'll eat a meat substitute, just in case she doesn't like them.
I would make some tofu instead of getting a fish substitute. Tofu is really good if you cook it right (well, I like it raw too), here's some ideas here:
http://herbivoracious.com/2012/05/how-to-make-tofu-really-freaking-delicious-tofu-101.html Its good if you cook it on a pan with oil (season beforehand) and cook til it's golden brown, its nice and crunchy on the outside, soft inside, and works well in a sauce, on veggies, or in curry (I like it in Laksa Lemak). If you don't want to do tofu, there's always bean dishes, falafels, eggplant, etc.
