My main website uses port 80/8080 (Apache with Tomcat). But running on the same server I run my own Atlassian JIRA bugtracker, Atlassian requires this to run in its own Apache tomcat server I cannot just deploy another application to the existing tomcat server so have to serve these pages on the 8081 port.
So there are no duplicate pages I just want to know if Google (and other search engines) would consider these as a single site or two sites.
Interesting question. First of all, if you really care about SEO you should probably not run sites on non-standard ports. I couldn't find any sources for this case specifically but in general Google cares also about user-friendly URLs. I don't think having an extra :8081 counts as such.
I found Doorways on Non-default Ports — New Trend in Black Hat SEO? from late 2010. I guess that Google has also picked up on this by now and is probably a bit more suspicious with websites served on non-standard ports.
Overall, you probably want to set up a virtual host on jira.example.com:80 that serves stuff from localhost:8081.