I'm gonna try to explain this as I understand it, so it's possible for somebody to disagree with some or all of my statement. But basically, a grappler is a character with a command grab at the core of their mix-up game. The term isn't super well defined, and some people use it a bit differently, but for the most part, a grappler is somebody who really wants to put you in a position where they're scared to hell of a really powerful command grab option. Like, if the command grab hurts so bad to get hit by that the other player will do just about anything to avoid getting thrown, then I'd say you've got yourself a grappler. Sometimes even to the point that actually landing the command grab becomes somewhat rare, because simply threatening the other player with it keeps them in line.
Simply having a command grab isn't enough. It's got to be at the core of their mix-up game. Having a really powerful normal throw isn't really enough either; throw beats "block high" and "block low", while command grab beats "block high", "block low", and "tech throw". That's what makes a grappler so scary if you let them get close. But if the command grab is slow enough to react to, or isn't very rewarding if you land it, then it becomes a situational tool. Q's command grab in 3rd Strike is pretty slow, to the point that he usually gets hit out of it, and the damage he ultimately gets out of it is decent at best. People don't even attempt that one very often, except after a parry, and then only because it's the best damage he gets off a parry. Compared to Iron Tager or Potemkin, who have command grabs that come out in like 4f and take off a quarter of your health and leave them in a position where they can threaten you with another mix-up.
To be clear, a grappler isn't a one-trick-pony. Nor is the command grab guaranteed if you get yourself into position to land it (reversals and jumping both avoid throws, backdashes in some games also avoid throws). The message sent by a grappler is basically "don't get complacent on defense, or get sloppy and leave gaps in your pressure, because if you do, you're going to wish you got hit by a truck instead".
Paprika has a command grab in TFH, but honestly, it's basically just a slightly slower, slightly riskier normal throw that you can't tech. Her normal throw is "okay", and her command grab is barely any better, and even then is still outperformed by her normal throw in some situations. It's not especially scary, so it's less "the core of her character" and more "a neat trick she can do".