Thanks Ron. What I was getting at is that they are the same species. Not different from a white rose & a red rose being the same species.
Within that, the way a person makes a recipe may determine whether they call them Limas or Butter Beans. Can you find a reference that exactly separates a Lima from a Butter Bean. Color, size, or shape? I've looked at several sites, some say there's no difference, some try to use size & shape as a difference. You can buy large & small Lima Beans, you can buy large & small Butter Beans. They are both Phaseolus lunatus.
In a similar manner, Luther Burbank developed over 150 types of green beans / dried beans. All different, yet all Phaseolus vulgaris.
Maybe the best way to determine what to call them is to leave it up to the person who is preparing dinner for you.