My battery is dead, no one is around to jump me and I need food. I have a 12V 10A bench top power supply from radio shack. Can I just jump it and charge the battery or will it result in sparks and fires?

Can we say "Crispy Critters" here!! Not trying to sound sarcastic here firebirdjosh. But no, do not use that bench top power supply to try and charge your battery. Get yourself a decent battery charger, they are not that expensive and are well worth the money.

What would the technical differences be between the two units. Both would put out around 13V correct? I have no problem getting a charger, but I just need to get the car started to get buy a charger, haha.

Could it work, yes, well... Depends on how 'dead' the battery is. If it's badly discharged it would pull way more then 10A and possibly damage the power supply. Also, you'll never get a 12VDC supply to fully charge a 12V battery. Is the power supply more then 12V, like 14.5VDC? If so your in luck. You need to find a 12V-9V light that pulls less then 1A. Hook this up in SERIES with the battery. So you go from B+ on the supply THROUGH the light to the B+ of the battery. Then just ground to ground. A light bulb works great as a current limiter for charging. Just use a VOM to monitor current so you know when it's charged.

Its a 12V power supply but puts out 13.8V. Thanks for the tip!

Keep in mind that you should see the light bulb light up at first and then dim down as the battery charges.