Dead Key Changes...

Now, I am hooked up to my battery, and I have noticed the same thing... I'm going to take a wild guess and say this is pretty standard as the voltage will be higher with the vehicle running

 

Yes, surface charge on a fully charged battery is 12.4 VDC; with the alternator charging, the voltage will go up 1 to 2 volts higher. Have you ever looked at a quality aftermarket car stereo amplifier? They often list the amp's RMS output wattage at 12.5 VDC and 14.4 VDC. It will always read higher wattage with more voltage.

 

The red wire goes to the positive side of the battery, the black to the negative side of the battery. Simple.

 

+1 to what Mike said (and the others who explained how much higher the voltage is with the engine & alternator running). Just take a piece of 12 gauge zipcord, run it through a grommet in the firewall to the battery, put a fuse terminal in the red lead just before the battery, and then ring terminals on both leads. The ring terminals go to the battery bolts.
The fuse by the battery should be bigger than what the radio needs -- say 7 or 10 amps -- as its only purpose is to protect your new wire from a dead short along its length between the battery and the radio. At the radio end, leave the stock (2.5 or 3 amp) fuse inline in the red wire to protect the radio.

The problem with using lighter plugs for radios is that there are many more connections between the battery and the power jack. Each connection has the potential to loosen or develop a thin layer of corrosion or oxidation, which increases resistance. Resistance drops voltage as current is pulled through it, and lower voltage at the radio's input equates to lower power output.

For example, with VHF FM radios, a 10% drop in input voltage can equal a 50% drop in output power. With CB rigs, using some version of AM, the power varies with modulation (unlike FM) but the principle is the same.

But it's not that hard. If you're able to wire up a cigar plug to a radio's power lead, you can do the fused battery lead.

You'll also find that your noise level, both on transmit and receive, is a bit lower, because the battery serves as a noise filter. But any resistance (remember all those connections going to the lighter jack?) tends to isolate the load (your radio) from the battery, and noise is allowed to stay at the radio.

When I drove a company vehicle, I wasn't allowed to add any permanent wiring or roof holes, so I got by with a mag mount and cigar lighter plug. But my radio, capable of 10, 25, and 50 watts by power switch, had to remain on 10 watts so I didn't exceed what the system would supply me. OTOH, I *did* use a really skookum antenna, which helped on both TX and RX.