Words Mean Things -- Science Meets Art Meets Life
Anyway, as Revere points out, infectivity is the precursor to pathogenicity. It refers to a virus' ability to get inside a cell and start cranking out copies of itself. As The Reveres explain, viruses are often picky about which kinds of cells they like to get inside:
If the host has a lot of different kinds of cells and tissues (as humans do), it is usual for the virus to restrict itself to one or a few types of cells. In humans, for example, the influenza virus seems to infect mainly cells within the respiratory tract and only some of the cells, at that.
Revere has talked before about which cells in particular various strains of influenza (for instance) seem to like, in exhaustive technical detail. Since I'm a rhetorician, dammit, not a biologist, I'll leave that for Revere (and while you're at it, go check out PZ Myers' Pharyngula).
Anyhow, even the ability of a virus to get inside a host cell and start using it to make print runs of itself doesn't guarantee that the host organism will be adversely affected. The ability to cause adverse effects -- disease -- in the host organism, is called pathogenicity. So, for instance, when you hear someone talking about a pathogen, they mean a disease-causing agent, but pathogenicity is also affected by extrinsic factors, like the host's health, the environment, and so on. As Revere says, "Pathogenicity (the ability to cause disease) is thus not something inherent in the virus but a combination of virus, host and environment." Some viruses can be quite infectious, but don't actually cause disease. (For instance, most cases of West Nile virus are asymptomatic, and up to 30% of influenza cases are, as well, which scares the crap out of me in the context of H5N1.)
However, if the organism does cause disease, whether it's mild or severe is a measure of its virulence. A virulent virus causes severe disease, a non-virulent virus causes mild disease. (For example, Ebola is virulent, but the common cold is not.)
And finally, Revere wants to remind us all that "pathogenicity is not the same as transmissibility. Transmissibility refers to the ability to pass from one person to another." Epidemiologists like Revere will be pleased to tell you how they measure transmissibility (using a value called an "R number"), but that's again tangential to the point.
The point being, of course, that nuance and specialised terminology exist for a reason, and careful writers (and speakers) should take care with language. Despite all the mocking around for quibbling over what the definition of "is" is, it's actually a good idea to be conscious and aware of language. The more self-conscious you are about your language, the more aware of it you become, the better you can present yourself to your audience, whoever that might be. If nothing else, it'll save you from becoming another Peter Beinart.