Yes, it is difficult to draw lines. That is probably as much of a reflection of the underlying science than anything, though. Biomedical research is messy. There is a lot of overlap between fields yet there is tremendous depth as well.
I make a somewhat arbitrary distinction between "bioinformatics" and "medical informatics". I see the former as relating more directly to wet lab support: munging data files from lab equipment and public databases, performing basic statistical analyses, etc. Lower-level stuff. Medical informatics (in my mind) focuses more on translational medicine. It tends to concentrate on higher-level concepts and the relationship of them to medical knowledge. Whereas someone in bioinformatics might work on highly specialized projects that support tightly-scoped research (e.g., specific genes, pathways, regulation, biomolecules), those in medical informatics tend to look at how low-level research from many sources can be integrated and translated to something that can more directly impact the standard of medical care (e.g., systems integration, knowledge management, data mining and inference, all from the level of a gene to a multi-center clinical trial).
Just to muddy the waters even further, I view "clinical informatics" as a field that supports and focuses on things related directly to patient care. That sub-specialty tends to be much more dependent on IT knowledge than biological knowledge (e.g., electronic health records, portals for patient access, billing, etc).
These definitions and distinctions are arbitrary and, in many ways, artificial. Ultimately it is experience that will define your professional career and get you your next job, not the words you choose to put on your resume.
In regards to your last point, I definitely think that is true. I think I'm getting caught up in trying to explain things that I lose sight of that. My reasoning though is that if I cannot explain something, it is probably a reflection of my own lack of understanding. So having troubles putting these things into words is a sign to me that I have yet to fully grasp what it is I am doing.
Thanks a lot for your replies. Really helpful stuff : )