W2 has different address from present primary address

The address information would only be important if the employer was mailing them to you. But if you will be downloading the documents, then the address on the W-2 form is of zero importance.

The thing that links the data to you is your social security number or tax id number, it isn't the mailing address.

If this is your current employer you do want to update your adress information, so that if they do mail you something it will get there.