They are not actually that different.
Both start out the same way - you can't have a handgun or a long gun - at all, anywhere at any time, in any condition
But then the carve-outs begin.
You can't have a shotgun or rifle unless you previously obtained an FPIC. However, the next line says you can't have a loaded shotgun or rifle.
You can't have a handgun unless you have previously obtained a permit to carry a handgun (hen's teeth, but the provision is in the statutes). This is the difference between handguns and long guns. There is nothing saying that handguns must be unloaded at this point.
There are a bunch of other carve-outs based on job, such as armed services, LEO, etc.
Then come the exemptions. The above offences do not apply in the following circumstances. If you are not committing an act that would be an offence so far, you don't need to worry about the exemptions. You cannot be exempted from an offence you are not committing.
You can have a handgun or long gun at your home, place of business, other land owned or possessed, etc. No mention of loaded or unloaded so loaded is OK.
You can transport between exempted locations, BUT you have to be travelling directly to/from, the firearm must be unloaded and cased, in a securely tied package, or locked in the trunk. This applies equally to handguns and long guns if you don't have the required permits.
Now, how does this apply to truck guns?
Unless you have the unicorn - a permit to carry a handgun - you cannot have a handgun as your truck gun. Ah, let's move on.
If you have an FPIC you can have a shotgun or rifle with you almost anywhere, but it must be unloaded. You can have loaded magazines separate from the gun. The whole story of not keeping loaded mags while travelling was a theory put about by a well known lawyer because there was nothing saying that a loaded mag could not be construed as a loaded gun. The NJSP have since said in writing that loaded magazines are OK to transport so that theory is now put to bed, or so one would hope.
A non-NFA other is neither a handgun or a rifle or shotgun so none of the above applies. As a previous poster stated, it comes down to any other weapon and whether you can show that you had a lawful purpose to be in possession of it. There is no case law as far as I know and no guidance from the AG. (Please don't go and ask him, PLEASE!!!!)