I own both Colt and Remington style clones, and agree with the coments of mcwoodduck and bedbugbilly.
If you are planning on only one of the two, be aware that the 1862 Pocket pistols could be described as the 32 auto pocket pistols of their day.
They are rather small, about 1/2 the wieght of the full sized designs, Are only 5 shot, and are rather under powered. In the old days, they were concealed carry guns, and were designed more for being discreat, than being well armed. Mine is fun to shoot, more accurate than I am, and I would hate to part with it, but a holster gun it is not. If I could only have one, I would chose the Remington, because of the extra power, and the fact it is just plain easier to control and hit with.
The 36 Remington has 6 shots, and full loads contain about twice as much powder as the pocket pistols. They are much more practical when it comes to holster carry or plinking time.
I would guess Pietta used "New Army Police", because other companys are using the "Navy" designation, but would bet they are pretty much the same guns.