How can I have conditional content within page body that is dependent upon the domain?
The sites module has support for multiple domains and managing content across those domains. 

https://www.drupal.org/project/sites

If you are using the same template file for the page where you are displaying your content, then you can implement the 'hook_site_access()' from the sites module in the template file, and gather the content you desire to display based on the domain name.

In addition, depending on the type of content you are displaying, you might be able to get away with simply using the Views or Context integration from the Sites module, rather than editing your template file manually.

Another option is to use Drupal's taxonomies to classify your content. Then, you could use any of the solutions above (custom code in page template, Views, or Context) to filter only the content which is categorized to be displayed on the domain you are on.

In any case, if you want two different versions of the same page to display on different domains, you will need two different nodes, and they will need to be classified accordingly. I'm not sure if there is any way around maintaining multiple nodes if the content varies by domain. 

However, when the same node is to be displayed on multiple domains, this kind of architecture will allow you to display it only on a specific subset of domains you choose.