回复：doesn't matter

The 秘书 is correct. Since you are pending on I485 adjustment; all you need is renew the EAD every year. But H1 can expired. You can have part-time job in EAD but not in H1b. Although your wife is H4, but EAD allow her to work if she choose otherwise.

When you have your Green Card , you need report to social security to have the Number Changed. The number on the EAD is for Tax purposes. MY father-in-law live in China have one, I use it for tax deduction.