I can't find this information clearly explained on Apple's website.
Apple Watch requires the presence of an iPhone to run third-party apps. Creation of a third-party app requires two separate bundles: a WatchKit app that runs on Apple Watch and a WatchKit extension that runs on the user’s iPhone.
also
Because a WatchKit app extends the behavior of your existing iOS app, the WatchKit app and WatchKit extension are bundled together and packaged inside your iOS app bundle. During installation of your iOS app, the system prompts the user to install the WatchKit app when a paired Apple Watch is present.
I assume it means that in order to create an Apple watch app I need to create a full iOS app first, with all the UI, resources and interactions. Is this a correct assumption?
Yes, this assumption is correct, in order to build apps for the Apple Watch, you need to build an accompanying iOS app. The explanation of this is in fact in the parts of the documentation that you quoted:
Because a WatchKit app extends the behavior of your existing iOS app, the WatchKit app and WatchKit extension are bundled together and packaged inside your iOS app bundle.
However, your description of a full iOS app, being one with "all the UI, resources and interactions" might be a bit misleading. Of course an iOS app does have such things, but the extent to which it makes use of them is concern of the developer (restricted by Apple's Human Interface Guidelines). so, the term "full iOS app" sounds a bit strange and doesn't really mean anything :)