Okay, I don't know why I didn't understand this before (end of week? Sleep deprivation?), but this document states quite clearly in the introduction, second paragraph:
There are two application routes to Nova Scotia Demand: Express Entry
stream, either you apply directly to Nova Scotia Office of Immigration
(NSOI) or you have been selected from the Express Entry pool by the
NSOI. In either case the principal applicant will need to submit a
complete application to NSOI.
So, if you've already applied to the national Citizenship and Immigration Canada (CIC) Express Entry process, send copies of that application as part of your NSOI application.
This is also stated on the originating page:
STEP 2: Complete the CIC forms and provide photocopies with your NSNP [Nova Scotia
Nominee Program] application.
This is specifically for the Nominee Program, where Nova Scotia thinks you'll be an excellent addition to the province and tells the national government, "Hey, we want this person!"
From what I can find, Nova Scotia can also look in the CIC Express Entry database for applicants who've stated they would like to emigrate to Nova Scotia and if the province likes what they see, invite them to apply or ask the federal agency to include them in the draw. In this latter case, I'm not sure if you have to directly apply to NSOI as well.