Warning -- I haven't had coffee. What is the difference between a primary contact for customers and the email address on a customer record? In other words, what determines which email(s) is pulled for what purpose(s)? Does it matter if the email address for a primary contact is different from the customer email address?

Email in Entity (Customer, Vendor, Partner, Employee) is the base email for the entity record, that means any communication to entity record will use that by default. Primary Contact is a contact record set as primary for the corresponding entity record, you use this contact for communication note that in this case it will be a named contact not the base entity. Yes you can have same email for both.