FWIW, IMHO, that category would be far off base.
Application Service Provider (ASP) software is another term for SaaS (software as a service). While there isn't an explicit industry consesus out there, the feel one gets is that smaller app providers still use the Application Service Provider nomenclature, and bigger products, Wall Street, and M&A firms use the SaaS term.
In either case, these are applications that run off the Internet, they are generally subscribed to, and they generally don't require anything except a browser and an Internet connection (usually no installs are required, but if they are, it would only be small widgets). In the last few years, the SaaS piece of the software pie has exploded, and thus, this has become a widely used, very general term that covers a huge sector of the market, from picture album managers, to Google Apps, to SalesForce.net.
PSA software packages are basically ERPs (entreprise resource planning systems) for anyone that has a company that performs professional services (e.g. bills by the hour like lawyers, accountants, architects, IT, etc.).
Like ERPs, they are big software that runs every aspect of your business (which, by the way, is why my recently suggested site doesn't really apply as it mainly covers billing, payroll, and time tracking).
Where ASP and SaaS are horizontal market terms, Professional Services Automation is a vertical market term (and, in fact, doesn't necessarily equate to software, as there might be a Professional Services Automation programmer, or a Professional Services Automation effeciency expert).
PSA software is a tiny portion of SaaS, and I'm pretty sure (although I would have to research it to be sure), that most PSA software are not SaaS products.