Is there a difference between using a built in SPI module and bit-banging?
An actual SPI controller peripheral in the MCU can often run much faster than bit-banging the interface.  Of course, it depends on the MCU, but it would not surprise me to see a SPI controller running at 30+ MHz, while bit banging might be limited to around 1 MHz (if you're lucky).

But there is more to it than that.  When bit-banging, the MCU is busy bit-banging it.  It is shifting the data out and twiddling the GPIO lines.  Meaning, it cannot be doing anything else.  When using a SPI controller, the controller is busy doing all that stuff and the MCU is free to do other things.  

So with an actual SPI controller, the actual SPI transfer is much faster and the MCU gains back some cycles that it can use to do other things.