I'm no expert here either, but i toss in my 2 cents as well.
Driving lights can usually be bought in two different patterns. You can either get a narrow beam, or a flood. It all depends on what you are looking to accomplish. If you want to see further down the road, you should probably go with a narrow beam that will project further down the road. If you are worried about something coming onto the road from the side, you should probably go with a flood pattern.
Fog lights: Hopefully this will make sense when i finish typing it out, if not...i'll try to clear it up. They are generally mounted low, and have an upper as well as lower cutoff on the beam. It will appear as if there is a band of light in front of the vehicle. Meaning, when you turn them on, there will be a space in front of the vehicle that is not being lit up, followed by a distance that is lit up, and then no more light. (I remember seeing a picture that better explained what i am trying to say, so i will try to find it) What this does, is reduce the amount of light that is reflected back up off of the road.
Running lights: I think Term3 was spot on with that explanation.
A couple side notes. If you do decide to upgrade/swap headlight bulbs, i would carry a spare set with you. The lifespan was shortened much more than i thought it would be, i found that out the hard way. I was in the middle of no where late at night when one of the bulbs decided it wasnt going to work anymore. Might as well be safe than sorry, and keep your old bulbs in the truck with you....just in case. The final thing is, dont go with blue/purple headlights. They do not throw the same amount of light that the yellowish bulbs throw.
2000 F350 lariat, crew cab, long bed, 4x4, 3.73 limited slip
LASB turbo from Irate Diesel
4" turbo back exhaust
Gauges (EGT, Trans Temp, Boost)
AFE Stage 2 XP Pro Guard 7
DP Tuner F6 (no start, stock, 80e, 60e, 60t)
AIH delete and CCV mod
F650 Dash with Carling switches
2002 Headlights with FX-R HID bi-xenon projector retrofit and 50W 5000K bulbs