Yes, the -c option specifies the methods of interacting with the device's loader.
The source code of the arduino programmer is http://svn.savannah.nongnu.org/viewvc/trunk/avrdude/arduino.c?root=avrdude&view=markup
Specifically, '-c arduino' chooses the client side code tailored to the bootloader in the Arduino Uno. Looking at the code in the above link, it tweaks the DTR and RTS lines to get the Ardunino into an stk500 compatible mode, and then invokes the stk500 protocol.