forms - 'same as shipping address' or 'different from shipping address'

In the order process we ask the visitor the address he want us to ship the ordered products and the address he want us to send the invoice

Most of the time, both are the same. We don't want the visitor to type the address twice in that case. after the shipping address, should we put:

☑ Send invoice to the same address

or

☐ Send invoice to another address

In both case the default is to no do anything if the address is the same. but is one better than the other? I think I like the second better but I can't figure if I'm right or why

-- edit:

in each case (shipping and invoice address), the user is presented with a dropdown to select an existing address, when one is selected, the complete address is displayed underneath. there is also an option to add a new address in which case, the block displaying the address is replaced by a a form where the user have to type it's address

but most of the time, there will be no form

Answer

In an online shop shipping physical goods you really need a shipping address, otherwise it's hard to know where to send the goods. In a few cases customers might want to enter a different billing address, but mostly not (make sure by doing some research in the existing customer database if you can). So it's preferred to give the option "[ ] Send invoice to a different address"

So you're right to default to both being the same which makes the form look much easier in the beginning. Those users actively selecting to enter a different address will not be surprised if the form has more fields after they ticked the checkbox. In other words, the default should be a checkbox that is not selected.

Addition:

The edit of the original question changes this from my point of view and opens up for another solution. How about displaying not displaying a checkbox but a dropdown? Default option in the dropdown is "same address". The other options are the other addresses that are stored in the system and would display the corresponding address if selected. The last option in the dropdown is "new billing address" which would reveal the form to enter a new address.

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