These days most threats do not fall into any single of these categories, almost all will fall into more than one. These are called "blended threats" or more often simply just malware. It's rare that you see malware that only can replicate itself in one way, that's why malware is such a problem.
To be honest these terms don't mean much anymore, as there are many threats out there that don't fall into any of these categories, or more than one of these categories. You have to expect that malware will have several methods of spread. Malware may first be run by an unsuspecting user opening a PDF file from an email, but then spread to other systems over the network and USB sticks. Or it may arrive in a USB stick and spread itself by emailing a PDF to all known contacts.