Hi Rachel! Dimensions vs measures and discrete vs continuous are two separate matters. Dimensions can be both discrete and continuous. The difference between dimensions and measures is (mainly) that dimensions are fields that are used to slice and describe data records (e.g. names, dates, IDs, geographical info), while measures are the value fields of those records that will be aggregated (summed, averaged, etc) to arrive at some final result.
One thing that you'll need to understand is that whether a field is a dimension or measure can be determined by your input, especially for numeric fields. For instance, notice that you can convert most numeric fields from measures to dimensions and vice versa. This is especially noticeable if you have any numeric ID fields, which Tableau tends to treat as measures by default, even though they should doubtlessly be treated as dimensions. Once you tell Tableau that a numeric field is a dimension, it treats it that way; it could just as easily treat it as a measure.
That being said, string and date fields can't be measures unless they're aggregated calculated fields.
Thank you for the explanation - however can you advise on the difference between dimension and discrete?