SQL - Difference between RANK and ROW_NUMBER

Ties between partitioning values will show you the differences, RANK will be the same on all ties while ROW_NUMBER will increment

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  

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