SQL RANK() versus ROW_NUMBER()

You will only see the difference if you have ties within a partition for a particular ordering value.

RANK and DENSE_RANK are deterministic in this case, all rows with the same value for both the ordering and partitioning columns will end up with an equal result, whereas ROW_NUMBER will arbitrarily (non deterministically) assign an incrementing result to the tied rows.

Example: (All rows have the same StyleID so are in the same partition and within that partition the first 3 rows are tied when ordered by ID)

WITH T(StyleID, ID)
     AS (SELECT 1,1 UNION ALL
         SELECT 1,1 UNION ALL
         SELECT 1,1 UNION ALL
         SELECT 1,2)
SELECT *,
       RANK() OVER(PARTITION BY StyleID ORDER BY ID)       AS [RANK],
       ROW_NUMBER() OVER(PARTITION BY StyleID ORDER BY ID) AS [ROW_NUMBER],
       DENSE_RANK() OVER(PARTITION BY StyleID ORDER BY ID) AS [DENSE_RANK]
FROM   T  

Returns

StyleID     ID       RANK      ROW_NUMBER      DENSE_RANK
----------- -------- --------- --------------- ----------
1           1        1         1               1
1           1        1         2               1
1           1        1         3               1
1           2        4         4               2

You can see that for the three identical rows the ROW_NUMBER increments, the RANK value remains the same then it leaps to 4. DENSE_RANK also assigns the same rank to all three rows but then the next distinct value is assigned a value of 2.