My wife has stage 4 colon cancer. One thing people who don't know some who has had cancer don't understand is that you can have it for a long time before it becomes so obvious that you have it. So while she has been far more susceptible to diseases before we figured it out, she found out because she went into the first stage of sepsis due to a necrotic tumor in her uterus that got infected. Sepsis isn't a disease, it's condition. Any infection can cause sepsis so it isn't a symptom but something caused by the symptoms, an add on effect, if you will. If not treated in time, you die of septic shock. Again, septic shock isn't a disease but a condition brought on by a disease. So no, dying from all diseases does not cover everything that you can die from that cancer or emphysema or COPD can have an effect on. In my wife's case, had we waited 24 hours more, she would have likely died because her organs would have started failing due to acidosis. Again, not a disease, a condition. Even if they had been able to treat her in time, her cancer would have likely made their treatments less effective than as they would have been for someone without cancer.
Let me try to put it in better terms. A disease can create a condition which can have a negative effect on the body. This condition is not necessarily solely caused by that disease, so it isn't a symptom. This condition, like acidosis of the blood, can then go on to create further problems, like organ failures, which you can die of. So in this example, the cause of death is organ failure, not acidosis, not the disease. and not the cancer. Without the cancer, the disease might not have spread as fast or happened at all. And thus, quitting smoking improves your chances of not dying from all causes, not just all diseases.