I know that this might seem counterintuitive to some because many forms of BDSM are "obviously" about causing pain in different and creative ways. But people don't do BDSM for the pain itself. They do it for where the pain takes them. They do it for the effect the pain has on them and on their partner.
At the end of a scene, no one says, "Oh [Insert name of cosmic being here]! That pain was so strong!". Instead they say, "That made me so horny!" or, "That was such a release and I feel so relieved!"
It can be easier, however, to claim that you do BDSM just for the pain because this can be a macho thing (or whatever the female equivalent is) which shows that you're tough! It's harder to admit that the pain gives you emotional release, helps you reach surrender, or helps you feel submissive, and so you just go into denial and say that you just do it for the pain.
Some people are harder to convince about this than others, but bringing out a house brick and offering to give someone as much pain as they want will usually get them on the path to confessing. Once you start talking house bricks, they'll say that it's not the right sort of pain, and then you are well on the way to them admitting that they need just certain forms of pain. From there it is just a hop, skip, and a jump to them saying that they need just certain forms of pain because these are what work for them. And there we are.
After all, if it were just about the pain, then a house brick is much easier to prepare and apply than setting up a flogging or whipping scene. There must be more to pain if someone is prepared to go the effort to unpack their toybag, do the scene, and then clean up afterwards.