Honestly, I believe everything is so relatively "new" that there really aren't any standardized descriptions. For example, you could enter both terms into a job search website, and their job descriptions could sometimes be interchangeable or very similar. That's why it is relatively convoluted in finding a job in one or the other.
When it comes to down to it however, the two are supposed to work hand in hand, but not be the same. For example, Informaticists, even clinical ones, sometimes don't need a clinical degree. They could have a Health or Clinical Informatics degree and certifications from AHIMA, HIMSS, etc. Consulting Analysts at Cerner Corporation do not need clinical experience, but Clinical Consultants do. However, a lot of their job duties overlap.
I completely agree that the specialties need standardization. When it comes to Health Informatics, the need for certifications and specialty training is becoming more and more prevalent (RHIT, RHIA, CAHIMS, CPHIMS, etc).
Essentially, the main difference, from what I've heard, is that Clinical/Health Informatics should be business-oriented, while Nursing Informatics should be patient-oriented. However, as how you've stated it, there is a great deal of mixing between the two. At this current time, there is no obvious, wide-spread delineation between the two to definitively say "this is this," and "that is that." Too many organizations are blending the roles to where there is no obvious difference. In theory and in academia, there are differences, but not currently in real time.
I am hoping that as we continue to utilize EHRs and technology in healthcare, we start to define the roles more specifically across the board, rather than just in textbooks or in organization-specific terms.