When you register a trademark, you do it for a specific region (country, EU...) and for a particular purpose (industry). In principle you could try to trademark a name everywhere in the world for every purpose imaginable, but it would be very very hard since any owner of an existing trademark can object if they think there is a chance of your name causing confusion with theirs and the resolution process can take time and be ultimately unsuccessful for you. So nobody actually does that.
Strength of a trademark really lies in both a) being registered and b) being actively used (first by you, but also by others). I think it is more useful to think of a domain as a digital equivalent of a sign hanged above the shop entrance. I think it affords you roughly the same level of protection.
IANAL, but I have registered a trademark years ago and had at that time spent some effort in getting acquainted with laws. They may have changed since.
If I use a trademark, say Ziglou, can I expect to have a right to every domain names with Ziglou?
Ziglou.com, Ziglou.net, Ziglou.org, Ziglou.some-new-top-level-name...
Can I expect to also have right to a top domain? Ziglou.ziglou?
Inversely, can one expect to have an established trademark just because of a domain name? In this case, HealthKit?