The way I see it, there are 2 types of physical pain:
Type A: The pain you feel when you fall off your skateboard, burn your hand on the grill, or have a headache - pain that you do not want to experience again. You may be willing to risk some pain in order to learn a new skill, such as riding a unicycle, but you still wear safety gear and try to avoid falling. Breaking your leg is type A pain because you need to stay off it in order to heal.
Type B: The pain you feel when you're stretching your muscles or doing something physically active that you enjoy, where even if you are in pain, you feel good at the same time. Continuing to feel the positive feeling is more important to you than avoiding the negative feeling, and the two are linked together to some extent. Continuing an activity such as stretching will actually reduce the pain, rather than making it worse. Having sore muscles is type B pain (assuming you didn't actually pull a muscle) because usually stretching the sore muscles will make you feel better.
Things do not automatically fall into one category or the other - whether pain is Type A or B is different for each individual. One person may be okay with some muscle pain that they experience going for a run, whereas another person may not be, even if the degree of pain is the same.
I think that these same classifications exist for emotional pain as well. Although it is a little trickier to define, most emotional pain or distress can also be divided into what you want to avoid, and what you don't mind or are okay working through. In this case, there is probably and even wider range of variation in terms of what people consider Type A and Type B. It doesn't really matter, but what matters is that we all recognize that there is a difference, that one person's Type A pain could be another person's Type B pain, and vice versa. After going through the same stressful situation, one person may feel exhilarated in a positive way, like they just finished running a race, while another person may feel more like they've burned themself and never want to do it again.
Next time someone is talking about something stressful or emotionally painful, listen closely and you can probably tell which type of pain it is to them.