@Rank vs @Row_Number

So recently I was asked the difference between the two and my brain froze.  There are other phrases that come to mind, but the condition of frozen brain is more PC and I'm sticking to it.

Back on topic; SQL provides a few "Ranking Functions" that can be most helpful.  There is a subtle difference between @Rank and @Row_Number I will try to demonstrate here, starting with a table called "Inventory".  For purposes of demonstration, we will assume that we can have multiple records of the same inventory item at the same location with the same quantity.  Here is the Inventory table:

The following SQL exposes the difference in the two functions:

select recordid, productid, description, location, quantity
,rank() over (partition by produtctid order by quantity desc) as rank
,row_number() over (partition by productid order by quantity desc) as row_number
from inventory
Results:

Highlighted above are the @Rank and @Row_Number for ProductID 101 at Location 1. 
Notice, that for every Product 101 at Location 1 that @Row_Number increments by 1.
@Rank, in comparison, does not. Duplicates do not cause @Rank to increment.  On rows 1 and 2, the value of @Rank is 1 - these are the number 1 values.  ODDLY though, if we look on rows 3 and 4 (also duplicate records) we see that @Rank continues with a value of 3.  This is because there are 2 records in ahead of it.

Conclusion:  @Rank and @Row_Number have different outcomes when duplicate values are present for the Partition By and Order By clauses.