NON Empty vs NONEMPTY()

NON Empty:

Remove empty rows or columns from a query

To remove empty rows or columns from a query, you can use the NON EMPTY statement before the axis set definition

SELECT 
{[Measures].[Internet Tax Amount]} 
ON COLUMNS, 
NON EMPTY 
[Product].[Category].[Category].MEMBERS 
ON ROWS 
FROM [Adventure Works] 
WHERE([Date].[Calendar].[Calendar Year].&[2001]) 

NONEMPTY():

Remove empty tuples from a set

More generally, to remove empty tuples from a set you can use the NonEmpty function.

WITH 
MEMBER MEASURES.CategoryCount AS 
COUNT([Product].[Category].[Category].MEMBERS) 
MEMBER MEASURES.NonEmptyCategoryCountFor2001 AS 
COUNT( 
NONEMPTY( 
[Product].[Category].[Category].MEMBERS 
,([Date].[Calendar].[Calendar Year].&[2001], [Measures].[Internet Tax Amount]) 
)) 

SELECT 
{MEASURES.CategoryCount,MEASURES.NonEmptyCategoryCountFor2001 } 
ON COLUMNS 
FROM [Adventure Works]