Nbox is a preamp.
Baby Nbox is a battery box.
With Nbox you can use line-in on recorder.
With Baby Nbox you might be able to use line-in on recorder.. but might need to use Mic-in on recorder. I've never used Baby Nbox, but people seem to love it and some seem to be successful when going Baby Nbox to Line-in on recorder.
I've used Nbox+ in the past and had great results unless I had bad batteries.
This is an accurate description. Will add a few things that are useful. I have both and use them both. Each is a useful tool. Sometimes one needs a hammer and another time a screwdriver.
BabyNbox runs on 1 9 volt battery and is most useful when

in high security situations. Battery lasts a long time. I have never run line in with it on a Tascam DR-2D.
NBox Platinum is a redesign of the original NBox with enhanced battery life as the biggest improvement over the original NBox (50 hours vs 10 for 4 9-volt batteries). It is larger than the BabyNbox and depending on venue security and skills it may represent a challenge to get in for some. It has gain since it is a pre-amp but the gain is not adjustable which was not clear from an earlier comment.
The actives work with either box. Also recommend the metal connectors if stealthing. I broke the plastic connectors a few times but never broke the metal ones.