Although there are many definitions as to what constitutes kitniyot, the bottom line is that it all depends on the reigning custom (minhag). Rabbi Moshe Feinstein zt’l, the pre-eminent 20th century American posek, explains that once a minhag is established, it does not readily change, even if circumstances change.
For example, the minhag was to allow anise seed and coriander, because they were not grown near wheat. Although their growing patterns and geographies changed over time, both anise seed and coriander continue to be accepted as non-kitniyot, provided that one is extra careful to check that wheat is not mixed in.
Similarly, potatoes and tapioca are not considered kitniyot. Although today, they are turned into starch and are the basis for most Passover cakes and cookies, they are permitted because, historically, the minhag was to accept them.
There are several grains/seeds for which differing minhagim exist. For example, some Ashkenazim will eat peanuts on Passover and others will not. The same is true for cottonseed oil. In America the widely-accepted minhag is to accept cottonseed oil as not kitniyot, though there were prominent American poskim who held otherwise. But in Israel, most kashrut agencies will not certify cottonseed oil. Rabbi Feinstein explained that if one knows that they have a particular minhag, then they must follow that minhag, otherwise they should follow the minhag ha’makom (local custom).