Here is a good definition of <a href=”http://www.webopedia.com/TERM/D/DID.html”>DID</a> while here is the <a href=”http://www.webopedia.com/TERM/P/PBX.html”>PBX</a>
They are completely different things. PBX is a system while DID is a service.
PBX is the company’s private phone system.
DID is a phone number which can be associated to your PBX. You can use DID numbers as direct dial numbers to specified extensions in your phone system.