Can we only use Primary Key and not Foriegn key while joining tables ?

I was trying a joining example provided in my book in which customer is a table and person is another table.

The query provided in the book is this...

USE AdventureWorks2012;
GO
SELECT c.CustomerID, c.PersonID, p.BusinessEntityID, p.LastName
FROM Sales.Customer AS c
INNER JOIN Person.Person AS p ON c.PersonID = p.BusinessEntityID;

This is the query that I did....

SELECT
      c.CustomerID,p.FirstName,p.MiddleName,p.LastName
FROM
      Sales.Customer AS c INNER JOIN Person.Person AS p
ON
      c.CustomerID=p.BusinessEntityID

ORDER BY
         p.BusinessEntityID;

Keys :-

Person Table

[PK_Person_BusinessEntityID]

[FK_Person_BusinessEntity_BusinessEntityID]

Customer Table

[PK_Customer_CustomerID]

[FK_Customer_Person_PersonID]

However,both of them gives a very different result set.But my question is why do we need to use the Customer.PersonID

instead of Customer.CustomerID. Is it really important to use one primary key and one foreign,is there any specific reason why the book showed c.personId=p.BusinessEntityId.??

Please help.

Thank