Well, some definitions I looked up, said that vegetarians are to not have animal dairy products.
@Ladyshopper23 did a nice rundown.
Personally, people need to do what they need to do.
I also will add the WFPB Vegan, which also are to not eat any oils, refined flour or sugars, or added salt. Yes, this extremely challenging on a cruise ship, but very doable at home.