Contextual and regional, but pop is more common (where I'm from) for your own father, whereas pops is what you might call an older man if you wanted to call them old.
I mean sure new slurs are invented all the time, but it's really not that deep. Pops is just one of the more common ones. You see it in movies and stuff.
E: I'm not even saying it's wrong to say, just calling it what it is