you can throw a splitter from a variety of different grips all of them are to reduce the spin of the ball while still throwing it at high velocity. the splitter is pretty much a boosted sinking fastball.
gripping it between the seams is usually used to throw a forkball which is the grandfather of the splitter.when you throw a splitter you just spread apart your fingers and fire it like a fastball. when you throw a forkball you spread your fingers even more so that you pretty much have the middle of the ball touching the middle of your 2 fingers. you throw it with a fastball motion but flick the wrist forward and give it either a slightly top spin or pretty much no spin at all. in either cases, the ball will dive suddently as it reaches the plate putting no spin on the ball will make it act like a fast knuckleball jumping around and diving but at more speed. jose contreras as some kind of forkball with an interesting grip which you might want to check out. using the seams for more grip resulting in a pitch going faster but still doing that whole forkball thing. and this pitch is a lot more off-speed than the splitter
if you throw a splitter it's better to be thrown with a 2 seam grip but for the forkball you could pretty much just grip it from anywhere and fire it. it's all about the wrist flick for that last one though.