Different terminology for discrete vs. continuous "marginal" concepts? e.g. Marginal Utility. 

If the good you're consuming is discrete, like "slices of pizza eaten", then authors (or at least the author of my textbook) talk about Marginal Utility at each quantity eaten as "the amount of extra utility you get from eating 'one more' slice".

If the good you're consuming is continuous, like "amount of juice drunk", then if you did that you'd just always get "an infinitesimal amount of extra utility, from 'the next' infinitesimally small sip". That's useless, so instead you use derivatives and ask what the instantaneous rate of change in utility is, with respect to juice.

Though related, these are different quantities, and they have different units ("difference in height" vs. "slope" of the total utility curve).

Do they also have different names?
I found an answer that satisfies me in Preston McAffee's Introduction to Economic Analysis (2006):


  Marginal is just economist’s jargon for “the derivative of.” For
  example, marginal cost is the derivative of cost; marginal value is
  the derivative of value. Because introductory economics is usually
  taught to students who have not yet studied calculus or can’t be
  trusted to remember even the most basic elements of it, economists
  tend to avoid using derivatives and instead talk about the value of
  the next unit purchased, or the cost of the next unit, and describe
  that as the marginal value or cost.


So it looks like economists don't have a terminological distinction, because in their own work they tend to treat all goods as near enough to continuous anyway (I suppose because it's easier and because markets are often large). The only reason they talk about e.g. the price of "one more unit" of a good, in introductory classes and textbooks, is that they don't expect the students to be comfortable with calculus yet.