Billing Addresses - Am I missing something?

Billing Addresses - Am I missing something?

I'm hoping this is simple and I am just not understanding the relationships between shipping and billing addresses correctly. 

1. We started with shipping (physical) addresses for accounts
2. We're now at the point where we want to add billing addresses. Sometimes they are identical to shipping addresses, sometimes they are not. 

- if shipping = billing, apparently there is a way to copy shipping to billing with a single button but no button shows up in the account layout. Am I missing something here?

- One billing address could be related to multiple shipping locations. Instead of typing in the billing address, can I not associate an existing billing address with a lookup?

Like I said - this seems to obvious that I must be missing something. Could someone point out and correct my obvious ignorance?

JV