Is there any difference between Samsung Galaxy S 3 GT-I9300 and I9300? I've been looking into flashing a custom ROM on my Galaxy S 3, and most of custom ROM are only supported by the I9300 model of the Galaxy S 3.

When I went into my phone's settings, it said GT-I9300, so my question is: Are these two are the same and the HTC part is just being omitted, or these are two different models of the device? 

Thank you for the attention, I.
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.