If you are using 8 or 9 (probably it is true for the 10th):
When you modify customer address in the admin screen you can mark adress as billing and shipping:
DB wise these are bit fields in the COM_Address
select AddressIsBilling, AddressIsShipping from COM_Address
Same thing happens during checkout: the customer has to enter address anyway so you must have a step with an address, but you just need to set AddressIsBilling, AddressIsShipping to true at the back end.
In the checkout process you have "Billing and Shipping Address" step where you are using the same "customer address" web part. Edit this step, change titles, remove checkbox "My shipping address is different from the billing address" and you good to go.
P.S. You can use 1-step checkout process if you looking for simplicity. E-Commerce site example has both check out processes (1-step and regular checkout). You can install and do some experiments there.