I know that the DIMM type describes the RAM that the motherboard accepts, but does it have any actual effect on how a computer runs? I'm considering this for gaming and can't seem to find much info on it.
One will fit and work, the other will not. DDR3 is 240 pin, DDR4 is 288 pin.
Yes but does that make any difference in how the pc will be able to run games or no?
DDR4 is faster than DDR3. So yes, it will make a difference. I don't know if it will be obviously noticeable. But the faster system RAM will have faster throughput.