Is there any difference between Samsung Galaxy S 3 GT-I9300 and I9300?
I9300 is just a shortened form of GT-I9300.  They both mean the same device.

Just don't mix it up with the I9305, which is a different device, specifically the international LTE version.

Wikipedia has a useful chart of the different models and how they differ.  Minor models (e.g. I9300/I9300T or I747/I747m) are inter-compatible for ROM purposes.