Unfortunately there’s no easy way to merge the design of both themes this way, but each theme is based on HivePress plugin (it powers all the functionality) so you can use listings, requests, vendors for any purposes within the same website (depending on its niche).
For example, you can enable Marketplace in specific listing categories only (if you use them as paid services posted by freelancers), and use other categories for job listings. If you use vendors as freelancers only, then you can try using requests as job listings (in HivePress vendors can add listings, while regular users can add requests).
I see that in JobHive the post_type=hp_listing is called “Jobs”, and the post_type=hp_vendor is called “Companies”, whereas in TaskHive the post_type=hp_listing is called “Listings”, and the post_type=hp_vendor is called “Vendors”. They also have different Icons.
Where can I adjust those settings? Is there a settings-page, or is this done in code?
Yes, each theme renames listings and vendors to match the theme niche. Please check how JobHive does this in jobhive/includes/components/class-theme.php file, it uses the hivepress/v1/strings and hivepress/v1/post_types filter hooks for example.