Continuous and discrete are mathematical terms. Continuous means "forming an unbroken whole, without interruption"; discrete means “individually separate and distinct.” Green measures and dimensions are continuous. Continuous field values are treated as an infinite range.
Tableau’s specialty lies in displaying data differently either in continuous format or discrete. Both of them are mathematical terms used to define data where continuous means without interruptions and discrete means are individually separate and distinct.
While the blue color indicates discrete behavior, the green color indicates continuous behavior. On one hand, the discrete view defines the headers and can be easily sorted, while continuous defines the axis in a graph view and cannot be sorted.
Discrete data is a count that can’t be made more precise. Typically it involves integers. For instance, the number of children (or adults, or pets) in your family is discrete data, because you are counting whole, indivisible entities: you can’t have 2.5 kids, or 1.3 pets.