Purpose of USB (FTDI) and ICSP connectors
The ICSP is used for 'bare metal' programming. This what you'd use if you wanted to replace or remove the bootloader, change the clock oscillator settings, or program the device as a bare 328.

The USB port is for communicating with a program running on the Arduino. When it's first booted, the bootloader program checks to see if there's any activity on the serial link from the Arduino host program on a PC. If there is, then it allows downloading of a program from it. If not, it continues on to the last code that was programmed into it.

The easiest way to see whether a bootloader is installed is simply to start it up with the PC host, and see whether it can talk to it.