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Continuous is the default for aggregations, and will cause tableau to draw an axis to plot marks on. Discrete will list each discrete value resulting from your calculation.
This is a good primer: Blue things and Green things - The Information Lab
There are two types of data roles in Tableau – discrete and continuous dimension.
- Discrete data roles are values that are counted as distinct and separate and can only take individual values within a range. Examples: number of threads in a sheet, customer name or row ID or State. Discrete values are shown as blue pills on the shelves and blue icons in the data window.
- Continuous data roles are used to measure continuous data and can take on any value within a finite or infinite interval. Examples: unit price, time and profit or order quantity. Continuous variables behave in a similar way in that they can take on any value. Continuous values are shown as green pills.