My research is supported by the Department of Energy, which is probably the easiest of the granting agencies to work with. They basically have an exclusive on my personal research time, and our interaction is essentially annual. I'm a theorist, so that also simplifies things a lot. So no, I don't include grants under research. For me, the grant renewal is a high-priority "other work" project. From talking to my colleagues, I know that other agencies, such as NASA, can provide a roller coaster ride requiring daily attention at times. From what I hear about NIH funding, two RO1's is doing pretty well right now. I have been involved in some large interdisciplinary grants, but those are collaborative efforts that feel much more like "other work" than personal research.
I have broken out Travel as a separate focus area (a Folder in Toodledo, which I am currently using) because that is driving a lot of my work right now. Of course, there is a lot of cross-over with research, but it is deadline-driven with lots of interacting parts, and mixes science (will this stuff be ready to talk about by then?) with administrative stuff (should I fly from Spain to Virginia directly, or stop at home to do laundry?). Something similar might work for grants for you.