ASP's are companies which let their software run on their own servers
and allow the subscribers use it. It has certainly several advantages
for both sides (no maintenance or hardware investment is required on
customer side, etc.)

In the end, products of ASP's are software products. Delivering the
software over the network is just another software delivery method.
For software engineers, it does not make the product less of a
software, for sure.

My question is, how the ASP products are categorized if they are
offered to government agencies? Are they still software products?
(Which I as a software engineer truly believe they are) Or is the
product placed in "IT services" category? Or even "Professional
Services" category?

Are there any federal laws addressing this issue? Or what is the logic? 

I would appreciate it if any sample cases are given.