Quick Answer
The difference between grams and cups is simple: grams measure weight, while cups measure volume. A gram tells you how heavy an ingredient is. A cup tells you how much space that ingredient fills.
Because ingredients do not all have the same density, the same number of grams can fill different cup amounts, and the same cup amount can weigh differently from one ingredient to another. That is why grams to cups conversions and cups to grams conversions always depend on the ingredient.