Assuming three levels of management, supervisory, mid-level, and upper level, in a typical organization, there is a difference not so much in the kinds of skills one needs as much as there is a need to address the small picture or the big picture, since as one goes up the ladder, one is responsible increasingly for the big picture and less so for the detailed picture.
Let's examine how that works at the supervisory level. The supervisor, sometimes called a foreman, is the lowest form of management. At this level, one has a group of people who are responsible for the production of goods or the provision of services, for example, in a factory or in a retail store. There is a great need for communication and people skills, since the supervisor is directly responsible for the operation, and he or she must communicate the tasks to be done and motivate the people to do the tasks. There is less need for planning skills, since overall plans have usually been addressed at a higher level, but nevertheless, this supervisor must be able to command the details of work schedules, delivery of materials, and so on. That is a planning skill, just at a lower and more detailed level. The supervisor must also have some technical skills, since there is a likelihood that the supervisor will be able to address low-level technical problems without calling in the IT department for every little thing, or at the very least, the technical skills necessary to identify that there is a technical problem. At this level, a supervisor also needs problem-solving skills, to troubleshoot the day to day problems that arise in the production of goods or services.
At the mid-level, managers are often in charge of departments that are function-based, product-based, or geographically based. Communication with the public, with other managers, with supervisors, and with upper management are central to this person's responsibilities. People skills are necessary, to motivate the supervisors below and to function well with one's peers and higher ups. Planning is of importance at a higher level, since this person is responsible for a bigger picture. Longer-range planning becomes important, as do plans for greater numbers of people and products or services. A manager of a large retail operation must be able to look beyond the work of the day, to plan what will or will not be sold in the future, what the trends are in the particular market. Technical skills can be important at this stage, although probably to a lesser degree. The security aspect, the protection of data, would require someone at this level to be technologically knowledgeable enough to know there was a security problem of some sort, for example. As a general proposition, though, this manager needs every skill the supervisor does, simply in a more big picture way.
At the very highest levels of management, communication skills and people skills are of the greatest importance. This manager is often expected to be the organization's "face" before the public, requiring highly polished communication and people skills. Management at the highest level requires motivating people, too, those who report to the manager, mid-level managers, for example. At this level, managers are expected to be role models, certainly, but the people at the bottom, those who produce or serve, are not generally in direct communication with this person. Planning for the highest level manager is comprehensive, making plans for the entire organization, and long term, thinking forward years into the future. This is a manager who is expected to assess all the opportunities and threats that the external environment provides, the person who needs to plan for various contingencies for the whole organization. Technical skills are needed at the very highest level, for example, in order to allow this manager to choose the best in systems hardware and software and to provide for privacy and security for the organization. Problem-solving skills are needed at the very highest level, for those problems that plague the entire organization.
All in all, the skills needed are the same at any level of management. The differences are a matter of degree.