Just my two cents, but if you have to dialog about the distinction between an "application" and "network" penetration test, then you're missing the point and not probably testing anything worthwhile.
First of all, the "network" is not an asset. It's a connection medium. Access to a set of cables and blinky lights means nothing. It's the data on the systems that use the "network" that are the assets.
Second, when a pen tester says they're doing a "network penetration test", they really mean they're going to simulate an attacker who will attack a traditional application-- a "canned" application (usually), like one that runs as a service out of the box on a consumer Operating System. It's more than just an authentication challenge (though it could be that). It's likely looking for software defects in those canned applications or commonly known insecure misconfigurations, but it's really still an application that they are testing. [In fact, the argument that a "network penetration test" is nothing more than vulnerability scan seems plausible to me.]
Third, when they say "application penetration test", they are typically talking about either custom software applications or at least an application that didn't come shipped with the OS.
Fourth, if you're trying to test how far one can "penetrate" into your systems to gain access to data, there should be no distinction. If a path to the asset you're trying to protect is through a service that comes bundled with a commercial OS, or if the path to the asset is through a customer product; it makes no difference. A penetration is a penetration.
Yet, as an industry, we like to perpetuate stupidity. This distinction between "network" and "application" penetration tests is such a prime example.