Why does Rank() have gaps and Dense_Rank() not have gaps in ranking ties in rows?

Question

Then encircled rows in the Rank / Dense_Rank examples below have ties for TotCnt.  Ex1 (using Rank()) has ties for TotCnt=19 and TotCnt=20.  Then TopCustomers rank jumps from 4 to 6.  In Ex2 (using Dense_Rank() for same set) has the same ties
but the TopCustomers rank goes smoothly from 4 to 5 and so on incrementing by 1.  Why is this?  What is different from Rank() vs Dense_Rank()? 
Use Northwind
SELECT RANK() OVER (ORDER BY TotCnt DESC) AS TopCustomers, CustomerID, TotCnt
FROM (SELECT CustomerID, COUNT(*) AS TotCnt
FROM Orders Group BY CustomerID) AS Cust
SELECT DENSE_RANK() OVER (ORDER BY TotCnt DESC) AS TopCustomers, CustomerID, TotCnt
FROM (SELECT CustomerID, COUNT(*) AS TotCnt
FROM Orders Group BY CustomerID) AS Cust
Rich P

Answer 1

DENSE_RANK() "Returns the rank
of rows within the partition of a result set, without any gaps in the ranking. The rank of a row is one plus the number of distinct ranks that come before the row in question."
Basically, DENSE_RANK() counts the number of distinct ranks prior to the current one, and adds one to it to determine the new rank. 
https://msdn.microsoft.com/en-us/library/ms173825(v=sql.110).aspx
RANK() "Returns the rank of each row within the partition of a result set. The rank of a row is one plus the number of ranks that
come before the row in question."
Basically, RANK() counts the number of ALL ranks prior to the current one, and adds one to it to determine the new rank.
https://msdn.microsoft.com/en-us/library/ms176102(v=sql.110).aspx
That difference is the reason for the two functions.
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