This is the term used for ritualized suicide, usually to remove any and all dishonor from your family/clan/ancestors so that you will leave pure within your family. You disembowl yourself, making three cuts without any noise, and your 2nd will remove your head, helping you to preserve your honor if you successfully make your three cuts without a sound. If you do make a sound, however, your second will sheathe his/her sword and allow you to suffer the pain as you slowly bleed out, having already failed to preserve honor.

Kanshi is the ritualized suicide meant to show your disagreement with a lord’s unjust order or verdict. No honor is gained, as sepukku is meant to do, but it shows how strongly you disagree with something. It may be deemed later that you have earned honor after your death, if the decision that provoked the kanshi is later revoked.
Jigai is the term used when referring to a female version of seppuku. This is where the samurai-ko will stab themselves in the throat to die honorably. Most women will tie their legs together so they do not kick uncontrollably in their death throes.