Joe, to be recognized either way both must be in the DNSes. Basically, they are separate web addresses, just as store.mycompany.com or careers.mycompany.com might be.

Originally, "www" was the subdomain used for web sites, but over time the domain name itself became the common way to reference the organization's web site (4 fewer characters to type was the motivator, I think, plus "www" is non-intuitive to an end-user). Most of the larger web site hosts will automatically define both for you, but organizations with their own DNSes often fail to do this. Find out who hosts the DNSes, and get them to define the other address too. (If the DNSes are within the organization, they may have made the mistake of using the base domain as their internal network. They can still make it point to their web site for people outside of their network, but it wouldn't work inside. PM me if you have that situation).