How different amperage could affect a rechargeable device? I have an iPad with it's own charger that has 2 components: a USB connection cable and an electrical adapter that outputs 5.1 V and 2.1 A.

Also I have a car charging device that is suitable for phones that can be charged via the USB data cable. This one has the fallowing output specifications: 5.1 V and 1.0 A.

My question is if it is safe for the iPad to connect it to the car charging device and if the difference in the current output would affect it's accumulator.
The iPad and other iOS devices are very good about only charging from appropriate voltages and currents. In fact, the iPad even is programmed to detect and show a not charging message in the status bar when it is connected to a power source with current too low. This is most commonly seen when the iPad is plugged into a computer that only supplies the normal USB current of 500 mA.

In your specific case, one amp at 5.1 V will charge the iPad slower than normal but still provide a useful charge even when the iPad is in operation. Should you be consuming a lot of data, a lot of graphics, and using GPS location you could possibly use more current than the one amp charger supplies, so just watch your battery level while it's charging and you should be fine.