I have placed phone orders on occasion with B&H when I have a few questions about the product. When I place the order, I immediately get an order confirmation via email (probably because they have it in their system) exactly like I do when I place the order online.
I think the numbers are different so they can track where the order was placed in the system.. Internet, phone, in-person etc.
I can't imagine that phone ordering somehow slows or speeds up how fast the order gets put into fulfillment after the credit card has been verified.