HI Ian,
The Update field in table action does not support built lists. You would have to use it in a loop and update one record at a time.
The reason why you received an error message when using = is there was no match and no field was update since no invoice number = "001121, 001122" and when using <> it updates all record because no record is equal to "001121, 001122".
One additional note, I would recommend not updating using Invoice number but instead using RecordID.
-Michael