Two different front pages?
You can do this by using the Domain Access module which is meant for creating a site (with one code base and one database) where certain content is accessible by DomainA and other content is accessible by DomainB. In your case you can set all content to be accessible to both domains and just change the site settings for the front page based on current domain. In D8 there is the Domain Site Settings module which makes this easier, but in D7 you should use Domain Variable to change site_front based on the current domain. 

This method will allow you (for example) to create two view pages or nodes or whatever (one for each domain) and display completely different content (or content in a different order) depending upon the domain.