@Kaarme : Honestly... just personally accumulated trends....
I just kept track of how frequently the different terms were used relative to the appearance of the creature in question... and "griffon" was used more consistently for the 4-lion-legged variety, while "griffin" was used for the 2-of-each variety more... but I've been seeing less consistent results lately than I used to. And I rarely ever bother with the spelling "gryphon", though I believe that was the original spelling (and I guess could apply to all of the above).
For that matter, I was considering trying to formalise a difference between the griffins with the eagle legs at the front (more common) and the ones with eagle legs at the rear (rarer).... or perhaps figure out some sort of pattern behind the appearance of those ears some of them have, but not others...
I'm pretty caught up on enforcing consistency as regards fantastical fauna, as using the same words to refer to different things all over the place is a fucking nuisance (if people just use whichever fucking word they please, that does NOT aid in communication at all). But in this case I honestly have no better basis than "this is what it seems to be the majority of the time"...
Strangely enough, I've had a fixation on griffons / griffins in particular for a while now... I think it started with Dragon Age: Origins... where the fact that Grey Wardens used to ride griffs became a bit of an in-joke, and I loved pestering Wynne for griff stories and whining that I wanted to ride one... AND THEN in Dragon's Dogma, the griffin there (labelled as a griffon, I believe) turned out to be the most epic fight in the entire game... and I got to ride it. =3
On a tangential note, I don't use the English word "Dragon" for a Long (Chinese) or Ryu (Japanese) either. They're not the same thing, obviously.