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Before posting I looked at the control panel to see what terms they used and they were "parked or point".
To clarify. The site is domain.org. Because some users are so conditioned to .com, I've purchased domain.com. The plan is to park/point so when someone types either domain.org OR domain.com they will end up at the same web page.
To expand the question a bit further. I've seen a couple of sites that have two domain names: domain-name.com AND domainname.com. The explanation given was that it was for search engine ranking.
At the time I considered doing the same thing (using a hyphen between the words) and contacted the web hosting company to ask about parking/pointing a second domain name to my site and how would search engine spiders would see it. The hosting company's response was that the SE spiders are not redirected from one domain name to the other. In fact if you type in either URL (domain-name.com or domainname.com) the URL that you typed appears that way in the address bar.
I hope that was clear...
Essentially, you have duplicate Web sites. I know of situations where this has caused no ill effect, but I know of more where it has caused serious problems.
What you want to do, I think, is to permanently redirect (301) the .com domain name to the .org site. When that is done and the .com domain is typed into the address bar, the browser will redirect the surfer to the .org site, and the .org domain will then appear in the address bar.
Ideally, all links, internal and external, should point to the .org domain.