[SPARK-19127][DOCS] Update Rank Function Documentation

## What changes were proposed in this pull request?

- [X] Fix inconsistencies in function reference for dense rank and dense
- [X] Make all languages equivalent in their reference to `dense_rank` and `rank`.

## How was this patch tested?

N/A for docs.

Please review http://spark.apache.org/contributing.html before opening a pull request.

Author: anabranch <wac.chambers@gmail.com>

Closes #16505 from anabranch/SPARK-19127.

1 files changed, 10 insertions, 6 deletions

diff --git a/python/pyspark/sql/functions.py b/python/pyspark/sql/functions.py
index d8abafcde3..7fe901a4fb 100644
--- a/python/pyspark/sql/functions.py
+++ b/python/pyspark/sql/functions.py
@@ -157,17 +157,21 @@ _window_functions = {
     'dense_rank':
         """returns the rank of rows within a window partition, without any gaps.
 
-        The difference between rank and denseRank is that denseRank leaves no gaps in ranking
-        sequence when there are ties. That is, if you were ranking a competition using denseRank
+        The difference between rank and dense_rank is that dense_rank leaves no gaps in ranking
+        sequence when there are ties. That is, if you were ranking a competition using dense_rank
         and had three people tie for second place, you would say that all three were in second
-        place and that the next person came in third.""",
+        place and that the next person came in third. Rank would give me sequential numbers, making
+        the person that came in third place (after the ties) would register as coming in fifth.
+
+        This is equivalent to the DENSE_RANK function in SQL.""",
     'rank':
         """returns the rank of rows within a window partition.
 
-        The difference between rank and denseRank is that denseRank leaves no gaps in ranking
-        sequence when there are ties. That is, if you were ranking a competition using denseRank
+        The difference between rank and dense_rank is that dense_rank leaves no gaps in ranking
+        sequence when there are ties. That is, if you were ranking a competition using dense_rank
         and had three people tie for second place, you would say that all three were in second
-        place and that the next person came in third.
+        place and that the next person came in third. Rank would give me sequential numbers, making
+        the person that came in third place (after the ties) would register as coming in fifth.
 
         This is equivalent to the RANK function in SQL.""",
     'cume_dist':