Both of these expressions are arbitrary "standard" measurements of quantities of fruits and vegetables - and, confusingly, they also mean the amount of one particular type of food one might eat at a meal - also known as "helpings". Reading the article, we learn that "a portion (closed-hand sized) of vegetables like steamed broccoli or spinach for example, is about equal to two FDA servings." However, let's say I am a greedy individual, and I like spinach very much. So, if I were helping myself to the lunch buffet, I might load my plate with a "portion" or "serving" or "helping" of spinach which is four times the size of the closed-hand size portion mentioned in the article, or eight times bigger than the standard FDA serving.
If I did the same at dinner, my consumption of spinach would have amounted to 4 portions/8 servings per meal, or 8 portions/16 servings per day.