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It is common for psychological tests to include multiple items with similar meaning. These items are then combined to form an overall scale score (e.g., depression or depressed thoughts). Multiple items with a similar meaning are used to increase the reliability of measurement, which is also important for validity.
I don't think there is a huge difference in meaning between the two items, and presumably they are highly correlated. However, they may provide slightly different connotations to different people. Thus, by having multiple items, the scale may have improved reliability.
I think that there is some difference, at least to me.
All emotions are results of thoughts.
Sadness is most likely a result of negative thoughts about past or future (and, therefore, disconnecting from present moment).
"Feeling unhappy" is often misunderstood, because people often mistake true happiness for external stimulation/excitement. So I think what people are experiencing, when they say they're feeling blue, is simple lack of excitement. It doesn't have much in common with happiness (which is almost the opposite - it comes from the inside and is permanent).