Its a seperate point to say its a 'feature' not a product and thus is not actually sold to anyone (and thus distinct).
Either way, in Australia, both parties would apply under Classes 9 and 44 which covers all computer software and medical services respectively. It's likely that Apple will win on class 9 as "Kit" is far better known in the software community than "HealthKit.com"; and arguably 44 too, depending on Healthkit.com's traction in the medical field.
It's unlikely that Apple's HealthKit and HealthKit's HealthKit would cause confusion in the market - but it makes a silly story to say that Apple's Health (which may have overlapping functionality with the preexisting HealthKit).
Gotta love the media.
Though I'm curious to hear from someone with more legal knowledge than me: would the fact that there's very little chance of collision between these names protect either party from legal repercussions?
Naturally, this same reasoning can be used to challenge the use of the same trademark in a different domain, something clearly accepted by law.
It's one thing to have theoretically defensible IP, and other thing entirely to actually be able to.
Assuming equal resources backing the legal teams, it would probably be sufficient that they are both forms of software, as all software trademarks are lumped together in the single category. There might be some sort of passing off action one way or another but it would be more likely to come from Apple than HealthKit.
There seems to be overlap between the Health app and Healthkit.com which I suppose is the real issue. Hard to tell if Healthkit truly got sherlocked though, because I can't tell what they do from their website past management software.