Passing SSO creds to another application

We have two sites with two different login pages and two different VIPs/APM policies and two different hostnames - www.example.com and www.project.com... would that option still apply??

Yes it would. Keep in mind though that options 1 and 2 above will "short circuit" any subsequent access policy evaluations. So for example, you have two different applications and you want to authenticate users to the second by virtue of authenticating to the first. You can simply share the session cookie with a domain attribute, or flow through the multi-domain config in APM, but once you have a valid session token from the first policy, all subsequent policies in other VIPs are ignored. If you wanted to do something extra in the other policies (an additional LDAP query for example), this too would be ignored. That may not be an issue in your case as you can usually grab everything you need from the initial authentication. But should you need something more distinct per APM VIP, then the 3rd option may be more fitting.