Could I get an explanation of what those specs mean? I'm also looking at flashes for my D300 (SB-600 vs SB-800) and don't know squat.
No ofence, but I'm surprized new people, just getting into photography are buying D300s. I saw the "D300" in the question an just assumed pointing out that the GNs were different would be enough.
Guide Number is
the basic spec that descibes a flash. Like "focal length" is
the basic spec for a lens. It is the first thing you should look at.
To determine the proper exposure when using flash you devide the feet between the flash unit and the subjet into the guide number. So let's say you buy a flash with a GN = 56 and now you want to shoot a subject that is 10 feet away. You would set the f-stop on the camera to f/5.6 Now lets say the subject is 20 feet away you would need f/2.8 but maybe your low priced zoom only goes to f/5.6 if so then a GN=56 flash is limited to 10 feet.
Now days with automatic cameras we no longer have to do the mental math in our heads anymore because the camera does it for us. Guide numbers were invented back in the days of flash bulbs before electronic flashes were available.
Modern flashes don't have a fixed GN. You can ajust the power but only up to some maximum GN. It is this maximum that is published as the spec. Most modern flashes even allow you to work "backwards" and let you set the f-stop and then the flash adjusts it's GN to match - if it can. People who work with studio setup s still think in terms of GN and mostly use manual exposure. It is really not hard to divide GN by feet because you don't have to be exact, only close enough, maybe to the nearest whole number. You can estimate.
The other Nikon Flash is the SB400. Costs alot less than even the SB600 but lacks a swivel so you can't aim it at the ceiling when doing vertical shots or at a wall when doing horizontal shots. But if yuo have a flash bracket and a sync cord the SB400 would work fine.