[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 <[email protected]>

Closes #16505 from anabranch/SPARK-19127.

Author: bllchmbrs

R/pkg/R/functions.R

@@ -3150,7 +3150,8 @@ setMethod("cume_dist",
 #' 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 \code{DENSE_RANK} function in SQL.
 #'
@@ -3321,10 +3322,11 @@ setMethod("percent_rank",
 #'
 #' Window function: 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.
 #'

python/pyspark/sql/functions.py

@@ -157,17 +157,21 @@ def _():
     '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':

sql/core/src/main/scala/org/apache/spark/sql/functions.scala

@@ -785,10 +785,13 @@ object functions {
   /**
    * Window function: 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 denseRank 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.
    *
    * @group window_funcs
    * @since 1.6.0
@@ -929,10 +932,11 @@ object functions {
   /**
    * Window function: 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.
    *