From a legal stand point there isn't anything different; you'd still be put on suicide watch and or end up institutionalize. This is a hot topic in bio ethics because doctors are put in situations in which it may be warranted to execute a mercy killing, assisted suicide, or Euthanasia; the difference in these cases and murder is the same as what Garif said bellow.
The difference is from a utilitarian ethics stand point: will this suicide cause less deminished happiness for a family involved, say a family left with incermountable medical bills; does a potential for recovery and chance of long term happiness out weigh the family; does a rule utilitarian protocol (a statute to determine what people do in similar situations) reflect how a society should run.
This is why utilitarianism is such a tricky determinant for weighing what is fair and just.
The Dax case is a good example of this. A man looses dad in a car crash and is suffering 3rd degrees burns in most places. He asks the first on the scene for his shotgun to commit suicide. Spectator refuses beginning the long road of his physician being begged to let him die. Eventually the man is happy that he is alive, while still defending patient autonomy or his denied right to choose to die in the first place.