I will be a little inarticulate here, specifically when it comes to innovation, what do we talk when we talk innovation internally. Depending on background, perspective, role, among other factors, it could be any of the above.
Capability I use it here within a very specific boundary, Honda’s example illustrates this point clearly, from seeing itself as an automobile maker, it sees itself as a power systems designer, with such a simple shift in outlook it has been able establish itself as a leader in many related fields like portable power, boat engines, etc. Technology companies confuse capabilities a lot, as there are too many of them. So easier way to classify further would be to pick specific business outcomes that gets affected by a technology. For example capability to A/B test designs, capability to cut down ROI with new technologies, etc… One of the popular side to this classification is seeing creativity in relation with innovation and trying to build creativity / creative talent internally, usually through training.
State is like “being pregnant”, a very clear yes / no, and it gets theoretical to philosophical to spiritual when the nature of state discussion starts, and some are inclined to this specifically, usually the ones that also pick on innovation as a concept at a mental level. Concepts are related and complexities from subsumption / differentiation plays here and really no basis needs to be given, as long as it makes sense as a valid argument. None of these 2 has any outcomes guaranteed and safely so. Else we have to wait for a long time for that state or the concept argument to end.
Department is a space, earmarked for all those innovation action, in Apple it happens to be the design department, in IBM it is either Sales or research, I can no longer tell which, in GE it happens in research. Mostly a centrally funded structure with clear mandate on outcomes and how the units will use those. But with availability of information across boundaries becoming easier, it is very hard to keep an edge from within one single department. Still a preferred choice for old, hierarchical companies.
Process/Action is the distribution of what used to happen within the department and making it easy for anyone to do innovation with clear steps and results. Behavior/Culture I feel enough has been said and is absolutely not my favorite, as I put personal responsibility ahead of popular inaction.
So whichever way you want to define innovation internally and classify it, some things do not change, those include “tasking” around whichever metaphor you picked, managing risks on action, investment and market, measuring outcomes and reporting it out to investor/bosses, of course responding to politics that is there in any human/social system among other action.