There never is only one answer to what an executive’s job is. The executive is one “element” in a system and a system is driven as well as slowed down by a multitude of events. Not all of these will be immediately visible, as is the case for example with power, feelings, or perceptions. Even more so when these vary from individual to individual.
How the executive’s job can be described is very much dependent on the context one is in and what goal one is seeking to serve.
When taking a very broad perspective on the tasks an executive has to work on, they can be regrouped in broad areas. In her book “Executive Coaching with Backbone and Heart” Mary Beth O’Neil defines them as follows:
Communicating the territory, that is, the purpose, vision, and goals of the organization to key constituencies, as well as outlining opportunities and challenges.
Building Commitment, building relationships, and facilitating interactions that result in outstanding team performance
Producing results and outcomes through the direct efforts of others as well as the executive’s own efforts
All three of them are interlinked and they are independent of the company size. What does regularly happen, however, is that the smaller the company is, the less clarity there is that there is a need for professionalism in attending to these tasks. And the more, executives will rely on their technical competence in executing the work.