Words.Count (on a range) returns an unfiltered value. It does NOT pass through the WordCount subroutine.
ComputeStatistics(wdStatisticWords) returns a filtered value. It passes the command through the WordCount subroutine.
This is a sentence.<p>
<p>
Where <p> is a paragraph mark.
Dim r As Range
Set r = ActiveDocument.Range
MsgBox r.Words.Count
MsgBox r.ComputeStatistics(wdStatisticWords)
The first messagebox (Words.Count) returns 7.
This
is
a
sentence
.
<p>
<p>
The period and paragraph marks are counted as words.
The second messagebox - ComputeStatistics(wdStatisticWords) returns 4.
This
is
a
sentence
The period and paragraph marks are filtered out by the WordCount subroutine.
As a further note, Words.Count (on a range or selection) will count empty cells in a table as a "word". ComputeStatistics(wdStatisticWords) will not. For example:
<p>
table with 2 rows, 2 columns...NO TEXT (cells are blank)
<p>
Words.Count = 8
ComputeStatistics(wdStatisticWords) = 0
Why 8? Because:
<p> = 1
Cell(1,1) = 2
Cell(1,2) = 3
ROW 1 end-marker = 4
Cell(2,1) = 5
Cell(2,2) = 6
ROW - 2 end-marker = 7
<p> = 8
The end marker for a table row is ALSO counted as a paragraph mark, and therefore is a "word" to Words.Count.