Martyrdom

Why is a martyr not guilty of suicide? The Christian church has approved of the former but not of the latter. Is it inconsistent?

No.

In the case of the suicide, the person committing suicide is violating directly the moral maxim to not harm oneself. Generally, the person committing suicide wishes to bring about something (peace, relief of burden to others, etc.) and so acts in such a way to attempt to bring those things to pass. But the suicide's justification is not sufficient, for in attempting to bring certain goods to be he is directly violating a moral maxim, or as some would say, a "basic value."

In the case of the martyr, the martyr does not directly violate the moral maxim to not harm oneself. The martyr does not directly bring about his or her own death. Rather, the martyr is responsible for, say, defying the wishes or commands of the tyrant to deny the Christian faith. It is the tyrant who brings about the death of the martyr.