It does depend on the email client you are using, but in Outlook or Thunderbird you'll need to create two account entries, one for each of the email address, despite them both going to the same SMEServer account. Then you can "choose" from which account to send it.
You can use email "rules" to arrange for the emails to be moved to one or the other of two folders, according to the "to" address. In Thunderbird I do this all the time (i have hundreds of folders).