But. On further reflection, this isn't really true.
Historically, many (probably most) bombers with whom we in the West have had to deal in the past, have not been homicide bombers. That is, they did not wish or intend to kill anyone. The IRA, for instance, would generally call in warnings when it planted bombs, so that the area could be evacuated and, they hoped, nobody would be killed. And in the USA, both the Weathermen and the bombers of abortion mills tended to set off their bombs at night, with the aim of minimising or eliminating fatalities. These measures didn't always work, of course, and the bombers were often justly convicted of reckless disregard for human life, but nevertheless their intent was not killing. Homicide bombing, i.e. terrorist bombing with the intent of killing people, has been far from the norm for most of the 20th century.
So it is meaningful to speak of bombers who do intend to kill as "homicide bombers", to distinguish them from bombers for whom the death of any person, if it occurs, is merely an unintended result of their recklessness. And yet, it is still useful to subdivide the category of homicide bombers into those who intend to kill themselves as well, and those who don't; and "suicide bomber" captures this distiction — I don't think there are any bombers who intend to kill themselves but not others, so "suicide bomber" should be taken to imply "homicide bomber" within it, with no need to specify.