Wires will always introduce a certain degree of voltage drops. Especially if there's a lot of current passing through it.

That is what's happening in your case. The cigarette lighter socket practically shares the same wire coming from the battery to power up all electrical and electronic accessories in your car. The more electrical load being used, the lower the voltage is across the +12V wire. In geek speak, that's Ohm's Law at work.

You typically get a more stable voltage when you get the reading directly off of the battery posts.