Guidance on the discrepancy between not praying over a martyr and the hadith of the one who killed himself

Question:
A questioner says: You mentioned (may Allah preserve you) that a martyr is not washed and no prayer is performed over him. Then the hadith in Abu Dawud regarding the Muslim who killed himself and the Prophet (peace and blessings be upon him) prayed over him was mentioned. What is the reconciliation of this?

Answer:
My brother, there are many types of martyrs. There is the martyr of the battle, who is killed in the battle. And there is the one who is wounded in the battle, transported, and dies in another place. This is considered a martyr, but he is not like the martyr of the battle; he is subject to the rulings for the dead. As for the one in the battle, he is subject to the rulings for martyrs: he is not washed, not shrouded, and no prayer is performed over him. There is also the woman who dies in childbirth; she is among the martyrs, and yet she is washed, shrouded, and prayed over. The martyr of the battle is specific: he is the one who is not shrouded except in his clothes, not washed, and not prayed over. As for the one who died in the cause of Allah but not in the battle, he is treated according to the rulings for the dead. Yes. And he has the reward of the martyrs; "martyr" in the sense that he has the reward of the martyrs. Yes.